Forest have just eight points from their nine games so far, and although they went into the game on the back of a win against Watford on Saturday, they were soon shellshocked by their hosts.
Rodriguez's first came after good work from Brian Easton on the left and his cross was headed back by Austin for the England Under-21 international to score.
Junior Stanislas was the creator of the second, crossing from the left for Rodriguez to score at the near post - and Austin could have made it three even before McCann stabbed home after Forest failed to clear a Stanislas corner.
Wallace made it four just before the break when he capitalised on Wes Morgan giving the ball away and fired in after a mazy run.
At half-time, McClaren had sat by himself for around 10 minutes in the dug-out while his players warmed up by themselves. Despite a better second-half showing, Forest were still heavily beaten.
Miller did get Forest on the scoresheet when he latched onto a long ball to score, but the Clarets had the final word when Austin's looping header from another Easton cross went in despite the best efforts of a defender on the line.
McClaren said: "At the end of the day, players cross the white line and they have to be responsible for performance so, yeah, we sent them out early at half time.
"It's for other people to decide about my job. But it's not about me or my job, it's about the team and, as normal after a defeat like that, we ask for a reaction.
"My assessment? Rubbish. Unacceptable for the fans who travelled.
"I didn't see it coming but it seems to be the story of the season - one step forward and three steps back. It's hurting us."
Full Time The referee signals the end of the game.
Inswinging corner taken from the left by-line by Lewis McGugan, clearance by Andre Amougou.
Lewis McGugan takes a shot from outside the area and strikes the post.
Effort from inside the six-yard box by Alex MacDonald goes wide right of the target.
Lewis McGugan takes a shot. Blocked by Chris McCann. Ishmael Miller takes a shot. Lee Grant makes a save. Outswinging corner taken right-footed by Lewis McGugan played to the near post, Jay Rodriguez makes a clearance.
Dean Marney takes a shot. Blocked by Wes Morgan.
Direct free kick taken by Ross Wallace.
Booking Luke Chambers receives a caution.
Luke Chambers concedes a free kick for a foul on Dean Marney.
Zavon Hines takes a shot. Joel Lynch manages to make a clearance.
The offside flag is raised against Ishmael Miller. Indirect free kick taken by Lee Grant.
Substitution Alex MacDonald is brought on as a substitute for Marvin Bartley.
Lewis McGugan takes a shot. Save by Lee Grant.
Substitution Charlie Austin leaves the field to be replaced by Dean Marney.
Substitution Zavon Hines on for Junior Stanislas.
Substitution Lewis McGugan comes on in place of Matt Derbyshire.
Jay Rodriguez is caught offside. Wes Morgan takes the indirect free kick.
Brian Easton provided the assist for the goal.
70:18 Goal scored
Goal! - Charlie Austin - Burnley 5 - 1 Nott'm For Charlie Austin scores a headed goal from inside the six-yard box. Burnley 5-1 Nottm Forest.
Jay Rodriguez takes a shot. Luke Chambers gets a block in. Inswinging corner taken by Junior Stanislas, clearance by Clint Hill.
Joel Lynch fouled by Charlie Austin, the ref awards a free kick. Free kick taken by Lee Camp.
Effort from the edge of the area by Charlie Austin goes wide of the left-hand post.
Robbie Findley produces a left-footed shot from deep inside the penalty area and hits the post.
Effort on goal by Marvin Bartley from just outside the area goes harmlessly over the target.
The referee blows for offside against Jay Rodriguez. Indirect free kick taken by Lee Camp.
58:29 Goal scored
Goal! - Ishmael Miller - Burnley 4 - 1 Nott'm For Ishmael Miller fires in a goal from inside the penalty box to the bottom left corner of the goal. Burnley 4-1 Nottm Forest.
David Edgar gives away a free kick for an unfair challenge on Ishmael Miller. Strike comes in from Radoslaw Majewski from the free kick.
Marvin Bartley gives away a free kick for an unfair challenge on Robbie Findley. Free kick crossed right-footed by Radoslaw Majewski from left channel, David Edgar makes a clearance.
Ishmael Miller takes a shot. Andre Amougou gets a block in.
Robbie Findley challenges Kieran Trippier unfairly and gives away a free kick. The free kick is delivered left-footed by Ross Wallace from right wing.
Free kick awarded for a foul by Guy Moussi on Marvin Bartley. Chris McCann takes the direct free kick.
Centre by Robbie Findley, save made by Lee Grant.
The referee starts the second half.
Substitution Radoslaw Majewski comes on in place of Andy Reid.
45:00 +2:08 Half time
Half Time The ref blows to end the first period.
Charlie Austin takes a shot. Joel Lynch gets a block in.
43:39 Goal scored
Goal! - Ross Wallace - Burnley 4 - 0 Nott'm For Ross Wallace finds the back of the net with a goal from just outside the penalty box to the bottom left corner of the goal. Burnley 4-0 Nottm Forest.
Ishmael Miller fouled by Andre Amougou, the ref awards a free kick. Andy Reid restarts play with the free kick.
The assistant referee flags for offside against Ishmael Miller. Lee Grant takes the indirect free kick.
Jay Rodriguez is ruled offside. Free kick taken by Wes Morgan.
Ishmael Miller produces a left-footed shot from deep inside the penalty area which goes wide of the left-hand post.
Corner taken left-footed by Andy Reid from the right by-line, Brian Easton makes a clearance. Jonathan Greening takes a shot.
Joel Lynch fouled by Charlie Austin, the ref awards a free kick. Direct free kick taken by Joel Lynch.
Ishmael Miller takes a shot. Blocked by Andre Amougou. Inswinging corner taken by Andy Reid from the right by-line, Joel Lynch takes a shot. Save by Lee Grant.
Ishmael Miller takes a shot. Matt Derbyshire produces a right-footed shot from deep inside the six-yard box which goes wide of the right-hand upright.
The assistant referee signals for offside against Charlie Austin. Lee Camp takes the indirect free kick.
Free kick awarded for an unfair challenge on Luke Chambers by Jay Rodriguez. Free kick taken by Luke Chambers.
28:03 Goal scored
Goal! - Chris McCann - Burnley 3 - 0 Nott'm For Chris McCann gets on the score sheet with a goal from close range to the bottom right corner of the goal. Burnley 3-0 Nottm Forest.
Junior Stanislas takes the inswinging corner, Marvin Bartley takes a shot. Lee Camp makes a save.
Substitution Robbie Findley joins the action as a substitute, replacing Chris Gunter.
Junior Stanislas takes a shot. Blocked by Guy Moussi. Inswinging corner taken right-footed by Junior Stanislas, Charlie Austin takes a shot. Lee Camp makes a save.
The assistant referee flags for offside against Matt Derbyshire. Lee Grant takes the indirect free kick.
Close range effort by Jay Rodriguez misses to the left of the target.
Ishmael Miller produces a header from deep inside the six-yard box which goes wide of the right-hand post.
Centre by Kieran Trippier, Clint Hill makes a clearance.
The referee penalises Ross Wallace for handball. Clint Hill restarts play with the free kick.
Assist by Junior Stanislas.
14:10 Goal scored
Goal! - Jay Rodriguez - Burnley 2 - 0 Nott'm For Jay Rodriguez finds the back of the net with a headed goal from close in. Burnley 2-0 Nottm Forest.
Clint Hill gives away a free kick for an unfair challenge on Charlie Austin. Ross Wallace delivers the ball from the free kick left-footed from right wing. The ball is swung over by Junior Stanislas,
Ross Wallace takes a shot. Clint Hill gets a block in.
The referee blows for offside against Joel Lynch. Lee Grant takes the indirect free kick.
Assist by Charlie Austin.
4:10 Goal scored
Goal! - Jay Rodriguez - Burnley 1 - 0 Nott'm For Jay Rodriguez finds the net with a headed goal from inside the six-yard box. Burnley 1-0 Nottm Forest.
Chris McCann fouled by Jonathan Greening, the ref awards a free kick. The free kick is swung in left-footed by Ross Wallace, clearance made by Clint Hill.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.