"Even though results haven't been great, I felt tactically England were maturing, but this is a step back to the dark ages of two lines of four.
"Don't like England playing this system. So easy to play against. Predictable and dated.
"It's not about playing in straight lines, it's about playing between the lines. Depth gives flexibility, passing alternatives, creativity."
Since losing to Italy in the quarter-final of Euro 2012, England have mostly used a more flexible system. In the 10 games since that defeat, England's record is five wins, four draws and one loss.
However they sit second in their World Cup 2014 qualifying group with four games to go, two points behind Montenegro.
England World Cup fixtures
6 September at Wembley
10 September away
11 October, Wembley
15 October, Wembley
Hodgson, whose side meet Brazil in Rio on Sunday, defended his strategy against Ireland, saying: "I can't be too disappointed with the way we tried to win the game.
"We were probing, trying all sorts of ways of getting around them.
"In terms of what we're asking the players to do, there were a lot of positives."
However, Match of the Day presenter Lineker was not alone in his criticism of England's laboured performance.
Former Tottenham manager David Pleat told BBC Radio 5 live: "What England lack, and it's easy to say this without Jack Wilshere, is a clever midfield player who can open the door: a Glenn Hoddle, a Paul Gascoigne, even a Chris Waddle.
Irish eyes smiling
The draw at Wembley stretches Republic of Ireland's unbeaten run against England to five games. England last won on 26 March 1985, with goals from Trevor Steven and Gary Lineker earning a 2-1 victory over the Republic, for whom Liam Brady found the net.
"Overall, it was a stiff performance.
"It lacked movement and variation. The media will have their say but the only thing that counts is what Roy Hodgson concludes from the game.
"It would be terrible if England didn't qualify for the World Cup next year. They're not in the hardest group but they've slipped up [in qualifying]."
Former England defender Danny Mills told 5 live England were "too predictable".
"When you look at it as a whole, I understand Gary Lineker's comments," he said. "Going back to a 4-4-2 - we haven't seen that for some time. But it's not really positions that make a performance, it's players.
"If anything, England were a little bit rigid at times. Also, you have to look at the personnel available to Roy Hodgson. When you look at the players that were on the bench, it is pretty weak.
"If Brazil are on form at the weekend then I worry that Roy Hodgson's side will be taken apart."
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