Barcelona built a three-goal lead through Xavi Espart, Lamine Yamal and a Yamal penalty before Levante hit back twice in the closing stages, with Karim Adeyemi's stoppage-time strike eventually settling the contest at the Ciutat de Valencia.
Flick said the start of the match had been the key to the result, but admitted he was to blame for allowing Levante back into the game.
"The best part was the start. We knew it wouldn't be an easy match. No excuses. The first goal was my fault, I wanted to wait until the break to make changes and I should have made them earlier," Flick said.
"We have to fight, survive these games. We have situations we need to improve, we'll talk about it. But I'm satisfied with the result of the match. They had a good second half, but I'm happy."
Flick said his side would learn from the lapse in concentration, pointing to a recurring pattern when Barcelona fail to maintain full focus.
"We'll analyse the match, as we always do. We want to do it better next time. It's the same in every match, if you don't give one hundred per cent, things like this can happen. But we survive," he said.
The head coach also praised substitute Karim Adeyemi's decisive contribution after coming off the bench.
"In this situation, he gave us his best. He made it 2-4. He settled the match. He fought. They were playing at home. It doesn't surprise me what he does. When he's focused, he's fantastic. I've known him for years. I know what he can do. He's special. He doesn't relax, he's always looking for the next pass."
Levante boss Luis Castro, whose side had gone eight matches unbeaten before the defeat, said the pitch conditions and searing afternoon heat had made for a difficult contest for both sides.
"We watered it, but if there's someone in the stands who's almost dying from the heat, there's one thing we can't do: cover the sun," Castro said. "We cut the grass, we watered the pitch, because we don't like to win by leaving the pitch in bad condition. Yesterday we came here. We didn't come during the week, even though we could have, because we wanted the pitch to be right. What we still haven't managed to do, and we'll try next time, is cover the sun."
Castro said his side's response after falling three goals behind reflected well on his players, even in defeat.
"The losses are losses, but we're hurting because we wanted more. We wanted to play to win, because Barca are a huge team. But we'd gone eight matches unbeaten, winning seven of them. So it hurts, because we wanted to win, but we also know we gave everything."