Aleksey Batrakov gave the Turkish hosts the lead in the 27th minute, but João Cancelo equalised just before half-time. Fermín López then put Barcelona ahead in the 49th minute, Anthony Gordon extended the advantage three minutes later and Karim Adeyemi completed the 4-1 victory in the 64th minute.
Flick was satisfied with the result and the way his players recovered from the setback.
“We are very happy with the result. We also played well in the first half. They had one chance and scored. We managed to come back, and that was very important.”
The Barcelona coach singled out Lamine Yamal, whose creativity helped transform the contest after the interval. The teenager did not score himself but supplied the final pass for two of the visitors' goals, repeatedly troubling Galatasaray as space opened up.
“Lamine didn't score today, but he provided the final pass for two goals and was excellent. He is an incredible player and very important for us.”
Flick also explained why he kept Yamal on the pitch rather than substituting him. The winger's physical condition and influence made him an important presence throughout the match.
“Physically, he is ready. He is an important player, and it is good to have him on the pitch.”
Pedri, meanwhile, offered an explanation for his withdrawal. The midfielder had been influential during Barcelona's recovery but asked to come off because he was feeling unwell, rather than because of an injury.
“My stomach was hurting, and I wasn't feeling very well. It was better to ask to come off and let someone else come on fresh.”
The Spain international believed Barcelona had been too impatient with their final passes before the break. Once the visitors began to move the ball more patiently and involve their attackers in dangerous areas, the game changed quickly.
“In the first half, we often rushed the final pass. When they take the lead in this atmosphere, it is difficult, but I'll take the team's reaction from the match. The second half was spectacular.”
Pedri also rejected suggestions that Barcelona lacked goals, pointing to the quality available across the squad, including players arriving from the bench.
“We have a lot of confidence. People were talking about whether we had enough goals, but we are showing that this squad has them. It is only the beginning of the season, so we have to keep going.”
The win extended Barcelona's strong start to the campaign and gave them six points from their first two Champions League matches. Flick's side will now turn to a demanding run of domestic and European fixtures, with Pedri urging the squad to enjoy the challenge while continuing to win.