Barca won 2-0 - via goals from Lamine Yamal and Fermin Lopez - to clinched the LaLiga title.
Afterwards, Flick said: "I think the second half of the season, especially, has been incredible. We haven't lost a single game, and that's great. Congratulations to the team, the club, and the fans. We're very happy.
"It's always very positive to be mentally strong. After the Christmas break, they helped us a lot. Winning the Super Cup gave us confidence. The players, like Frenkie (de Jong) and many others, have reached their peak, and it's great to see how they've improved. I'm very happy.
"Espanyol defended very well. They played in a very dangerous way for us, so I'm very happy with the victory."
I told the players to take celebrations inside
On celebrating on the Espanyol pitch, Flick admits he told his players to take the celebrations into the away dressing room.
He said: "I know what the situation is with what happened two years ago, and we wanted to leave the field and celebrate inside."
Flick also said: "This usually comes down to attitude, and we've always thought positively. When I look at the training sessions, the preseason... we have a different philosophy on how we wanted to attack, and the team adapted well.
"With Barça, you have to win titles, and three is great (Supacopa, Copa del Rey and LaLiga). I suffered after the semi-final in Milan, but with three titles, I think both the club and the players like me... there's something to be happy about.
"Espanyol played a good game, pressing well. When Lamine received the ball, he had someone on him. I told them at halftime that they had to be faster. When the opponent is closed down, you have to play faster."