Michael Chopra sent hopes of a fourth-round appearance soaring among Ipswich fans as he opened the scoring but Villa fought back with strikes from Darren Bent and Andreas Weimann.
While McCarthy was disappointed to exit the Cup, he insisted his players had done him proud and his priority remains Championship survival.
He said: "When I came, the remit was to stay up and that has not changed.
"Maybe a replay would have got in the way but you don't like to lose and, when we were 2-1 down in the final minute, I would have taken a replay.
"I'm stewing about the goal we conceded just after half-time to bring them level.
"It changed the course of the game and, if you give them opportunities, they have the quality to make it count.
"But I was pleased with our performance as a whole."
McCarthy confirmed he would like to sign QPR striker DJ Campbell on a permanent basis after his recent loan spell at Portman Road.
He said: "I spoke to him last night and told him I'd like to sign him. We will have to see what happens."