Shaun Wright-Phillips had put Chelsea in front as Avram Grant's team dominated the first half but Yakubu struck a brilliant equaliser 10 minutes after Mikel's dismissal and James McFadden hit the post with a shot from a very tight angle.
"The players were great," added Moyes.
"They hung in there in the first half when Chelsea played well.
"Chelsea are a very good team. Their movement and inter-changing of positions was fantastic, but we stuck in there and had chances in the second half, we were unlucky with McFadden's especially."
Chelsea's winner came after Lescott was caught stationary at the far post by Wright-Phillips.
Moyes said: "It looks like Shaun has his hand on Joleon's shoulder at the end.
"I thought Joleon was going to make up for it with his chance after that, but he's played well for us this season and he's got nothing to be worried about."
Mikel was given a straight red by referee Peter Walton after a sliding tackle on Phil Neville.
"If it is a red card then two or three players who got yellow cards deserved reds as well," said Chelsea boss Grant.
"But I don't want to say anything else about this decision because the players who played today deserve to be talked about.
"I understand why I'm being asked about this but I only want to talk about the way my players performed. I'm proud of them.
"We deserved to win. We created a lot of chances even after the red card. We showed good spirit even after all the problems."
But Moyes countered: "I thought the referee was fine. Semi-finals are never easy games to referee, I can't comment on the red card, but I thought he was fine."