Blackburn boss Steve Kean felt his side should have been awarded a free-kick before Liverpool's injury-time goal sealed a 3-2 win at Rovers on Tuesday.
Kean claimed Grant Hanley was fouled by Liverpool's Martin Skrtel before the ball was pumped back into the home box for Carroll to head home.
"Where Hanley should be when the ball comes back into the box is where Andy Carroll was," said Kean.
"That's tough because it's cost us a point and two places up the league."
Television replays showed Skrtel tangling with Rovers defender Hanley, who could not get back into position before Daniel Agger flicked Sebastian Coates' long pass on to Carroll.
A point from the action-packed Ewood Park encounter would have lifted third-bottom Rovers above nearest rivals Queens Park Rangers and Bolton and out of the relegation zone.
But the late goal and a fourth straight defeat keeps Blackburn deep in relegation trouble with five games of the Premier League season remaining.
Kean criticised his side's defending for Maxi Rodriguez's two early goals but is convinced his side will avoid the drop to the Championship.
"Tonight was a massive opportunity missed for us," he said.
"We felt the way we got back into the game, considering we missed a penalty, to get back to 2-2, we felt if anybody was going to score it was us.
"We've always given everything we've got in the locker and we've given a good physical performance [against Liverpool].
"I did feel we showed spirit and determination to get back into the game. We're creating chances but we have got to defend set-pieces better.
"We always look like scoring when we're in the opposition area but we've got to be a little more aggressive in our own box."