Ferran Torres (2) and Raphinha struck for Barca, with Serhou Guirassy scoring twice for the hosts.
Afterwards, Flick insisted his young team deserved the three points.
The match:
"We can be happy with what we did. We believed. The first half was wonderful, and after they scored we remained stable. Today I don't think we suffered, although Dortmund played very well. It's difficult to defend against them, but we did well. The goals were because we made mistakes. We can always improve. But today I must congratulate the team because they did great.
"We had good possession, we played calmly. Then with the entrance of Ferran, Fermín... they were direct."
Raphinha:
"He's not injured. He's just tired."
Second half:
"I think we played a good game. The first was one of the best, even though we didn't score. We were good with the ball. Dortmund have very good players and if you give them the ball, they make the game difficult for you and they score. But we were stable after the 1-1 and then we got the win."
Reaction:
"The win is very special. We knew that there was a lot at stake for both teams. If you win you take a big step towards the next round. We want to be in the top eight. There is another game on Sunday, and we will see how the players recover. But the bench is very good. Everyone who comes on must be 100 percent. Ferran and Fermín have combined. I am proud of all the players.
"This victory should give us confidence. There are many games and for many players the workload is extreme. They are all professionals. They recover well. They are 100% in training. Against Leganés, we have to play as focused as today and have everyone participate. Today we saw that the team is united on the pitch. But Dortmund have a very good team and it is amazing to play in a stadium with this atmosphere. I am happy to have seen so many Barça fans here."
Locker room:
"They are united. As a coach we like their mentality, the players care about their teammates. The atmosphere in the dressing room is very good. Everyone is happy. It was very important to win here."
Ferran Torres:
"When he scores he is very useful... he knows how to switch from defence to attack. He is fast. He has scored in the last three games. I liked it when he came in. The second goal was not so easy. I am happy for him. He has a very good attitude and a positive mentality, he even had that when he was injured. He always wants to improve. Today he did very well what we told him."
Ambitions:
"As we have done all season, we take it game by game. We have many objectives and we want to win as much as possible. Then we'll see what we achieve. The team has a good mentality. It's impressive how united the squad is. It's like a family. And the fans can be happy. On Monday I had dinner in Barcelona and there was a neighbour who told me that he would come and that we should please play a good game. They will come back happy. The last trip had been to Liverpool and the children were not very happy, not today.
"It's a long road. We want to be among the top eight, that will be the first step. There are still many games left. We're taking it one game at a time."
Return to Germany:
"It's very cold, we're not used to this cold in Barcelona. The stadium and the fans are spectacular. They celebrate with the team even when they lose."