The result leaves Barca in second-place on the Champions League table going into the knockout round.
Flick said afterwards: "I'm very happy with second place, it's a great success for the team. It was a difficult match. We could have defended a little better.
"Yes, that needs to be improved. We are happy to finish in this position but we need to work on many things and we are doing that.
"Yes, it was a great game of football. Atalanta defended very well. We learned a lot from this game.
"It was good. We wanted to change things in the second half. We finished second and that's great. It's a great success for the team and for the club."
He continued: "It's always good to think about the next game. We'll see on Friday what the mix is and what the draw holds. We also have to bear in mind that there are some big clubs that are not in the next round.
"It's always the same. If you think this could be a good opponent... it could end up being the toughest. Today I saw a lot of things that we did very well and others that we can do better."
Flick added, "I think it's a new format and the most important thing is that you never know what will happen. Now I can say that I'm happy with this format because we're in the top 8 and we have 15 more days to train."