Barca managed to win 3-2, thanks to an injury-time own goal for the winner.
Afterwards, Flick said: "Levante defended very well. They have very fast players. It wasn't easy. They had good chances in the first half. We changed things in the second half. The first goal we scored helped us; we gained confidence and fought until the end to get the three points.
"Of course I'm proud, why do you ask? We earned the three points, we believed in ourselves, and this victory helps us a lot. It wasn't easy because when they play like that.
"We didn't play perfectly today, but we have to appreciate what Levante did; they have fast players. We scored three goals and could have won. We have to talk and analyze. These games help us improve and know where we want to go. A season is a long road."
Marcus Rashford was hooked at halftime by Flick, though the German defended his performance.
He added, "Marcus had a few chances in the first half and showed he can help us. In the second half, we needed to make changes and we put Raphinha on the wing, and I think they were the right changes. The first goal changed the game."