Barca won 2-1 at the Metropolitano, with Eric Garcia seeing red, but lost the quarterfinal tie 3-2 on aggregate.
Flick said afterwards: "We're disappointed. We had the chance to make it 3-0 and then conceded that goal. We had many opportunities, but we didn't take them. We're disappointed.
"We played a fantastic game. We played with one less man. But the players were fantastic. I really appreciate what I saw today. We haven't had much luck. We have to accept it.
"We've talked about how to improve. In the first half, we should have scored more goals. We didn't expect their goal. Looking at both matches, we deserved to be in the semi-final."
On what is left for Barca, Flick says the focus must now be on the LaLiga.
He added: "The next step is to win La Liga, and we're on the right track. We have to keep going. We must maintain this mentality. We're disappointed. All of us.
"Winning the Champions League is a dream. We have to learn from our mistakes and improve. We're a young team. Next season, we'll be better."