Barca won the second-leg 3-0 at the Nou Camp thanks to goals from Marc Bernal (2) and Raphinha, but lost the tie 4-3 on aggregate.
Flick said afterwards: "We were brave and I'm proud. It was a spectacular match. We were one goal short, but we played very, very well. When you see Bernal, (Pau) Cubarsí, Gerard... young players at this level... they gave everything for this club. That said, we are disappointed that we didn't get that fourth goal.
"We had chances. Everyone was convinced of how to play. Everyone was fantastic. Bernal scored two goals, Cubarsí was also incredible. It's the mentality I wanted.
"They can be among the best in the world. I really enjoy watching the players."
The German added, "Step by step, there's still a long way to go in La Liga and the Champions League. We're focused on each match; there are matches every three or four days.
"We're focused on Athletic. We need to recover and concentrate on the work. The quality we've seen is there."