Villa lost 2-1 on Tuesday night as Matheus Nunes found an injury-time winner for City.
Emery said afterwards: “We lost, but we competed very well, and we reacted after the goal fantastic, scoring one goal, drawing and we were defending very well, competing very well.
“We didn’t concede a lot. Of course, they were dominating the second half, pushing, getting some corners offensively, but we were defending very well.
“We had as well our chances with Marcus Rashford to score the second goal, and the last minute as well, I tried with some substituted players getting good impact and trying to win the match, but they did the same, and they won.
“Of course, overall, we can feel proud of everything we are doing. The supporters as well, they were with us today here, because they know as well the importance for us to play in the Premier League and, through it, to get Europe again.”
FA Cup now the focus
Villa now turn to Saturday’s FA Cup semi-final tie against Crystal Palace at Wembley.
“Disappointed a little, but so quick, I am changing my mind and now we are going to focus on the match on Saturday,” continued Emery.
“We have a very exciting moment in London on Saturday with our supporters against Crystal Palace in the semi-final and we have to enjoy it.
“We lost, we have to accept it. Of course, we tried, and I’m so happy with how we competed, but it was not enough, and even getting one point was not enough for us.
“But now, change our mind, try to get a lot of information about this match and to use positive things and be really positive for Saturday, how we can continue in our way in the FA Cup.”