Speaking to MUTV, Fletcher stated: "It's a really disappointed dressing room in there. It's a massive blow, let's not kid ourselves, this is a bad result. There's a lot of angry, hurt players and we feel like we've let the manager and the fans down.
"I thought we were the stronger team in the first half and that was the point where we should have gone on and finished the game off, or definitely taken the lead. We never managed to do that and the red card gave them a great boost in the last 10 minutes, and they went on to get the winning goal."
The United no.24's vast experience may prove vital in overcoming this setback and Fletcher says the players must respond positively on the trip to the Stadium of Light.
"It's a League Cup semi-final, if you can't lift yourself for that then it's no good," he said. "We have got a great opportunity, we are away to Sunderland and we've got to recover quickly and lift ourselves. That's a massive game now."
Fletcher also praised the attitude of United's supporters inside Old Trafford on Sunday, with many fans cheering the Reds off the field despite the fresh sense of disappointment at the result.
"They're really sticking by us and that's great to see - we've got to repay that," he said. "When we got to the Stretford End there were a lot of fans clapping and singing for United. The players have got to see that and know that the fans are behind us and put performances in for the them, the manager and the staff. It's got to happen sooner rather than later and there's not better occasion than the semi-final on Tuesday."