Sir Alex Ferguson fielded a second-string side, who were still expected to advance to the semi-finals alongside Liverpool, Manchester City and Cardiff City.
But they were dumped out by an extra-time Glenn Murray header after a Federico Macheda penalty cancelled out a Darren Ambrose opener.
Speaking after the match, Evans, who was named captain in his 100th United game, expressed his disappointment but insists it's time to move on.
"We're very disappointed not to be in the semi-finals," the defender told MUTV.
"I thought we would go on after we scored. And going into the first period of extra time, playing towards the Stretford End, I thought we'd have a chance of getting a goal and seal it from there.
"But they went down the other end and scored against the run of play really. We had a lot of possession but we couldn't break them down.
"A lot of our play was in front of them and I think the only way we were going to get in was down the side, but we didn't manage to do that as well as Manchester United can. We didn't get a lot of crosses into the box.
"The games are coming thick and fast and the manager will need his squad. So we need to pick ourselves up and hopefully win on Saturday [at Villa]."
Evans added that while proud to skipper the side, the end result took away from the honour.
"Before the game I was delighted to be given the armband, but I'd happily take that away to have the victory instead.