The Reds took the lead in the quarter-final second leg at Allianz Arena, but it was only a matter of seconds before Bayern hit back and then went on to claim victory in the tie.
"We're bitterly disappointed to go out," Carrick told Sky Sports. "We put ourselves in a great position, getting the first goal, and then it was only 20-odd seconds before we conceded. That was a big blow for us.
"Even then we were still in the game and we had a chance when Danny [Welbeck] laid it off for Wayne [Rooney]. I don't know if it bobbled up or it was a bit quick for Wayne but it didn't go for us. They had a lot of possession around our box but we defended so well for long periods. At times, all it takes is for something to drop to them and, in the end, it did."
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