Marcus Rashford's brace was too much for Newcastle, with Anthony Gordon's late goal coming too late.
Flick said afterwards: "It's very important to start the Champions League with three points in Newcastle. We saw a very good performance from the whole team. The atmosphere was fantastic. It wasn't easy to defend, but we controlled the game. I'm happy with how we played and what I saw on the pitch.
"We told them we had to hold out for at least the first 15 minutes with a clean sheet. They're very strong one-on-one. We were very good throughout the match. I think we had 64 percent possession in the first half. Maybe we made too many mistakes."
On Rashford, Flick said: "He scored two beautiful goals. The header was very good, but the second one was also. The important thing is that he gains confidence. We're helping him. I'm not surprised by his performance.
"I said it yesterday, he's a fantastic player, he's very talented. His skills and finishing are very good. In the first half, he had chances and didn't finish. In the second, he did. It's important for a striker to score. He took advantage of his chances. We needed a player like this."
Flick also said of the Manchester United loanee: "He's taken the first step, he needs to take the second. Two goals here at home, on this pitch... it's an important step for him. He's shown he's a great player.
"He needs to take another step. I spoke to him when the opportunity arose and said I wanted him on my team, and I'm happy. He's outstanding. The team is also helping him. He has strengths like speed, finishing..."