The 17 year-old, full name Pedro Fernandez, was a surprise starter for their 2-1 win against Real Sociedad.
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Flick fielded Dro in the No10 role just behind striker Robert Lewandowski on the night.
He later said: "He's a very talented player. He's a Barça player.
"It's great to have these kinds of players to be able to manage minutes. I really like that everyone tries to give their best. This is what we need because we have a lot of games.
"It was a team victory. They knew how to play, and it was hard work, but we deserved it."
Barca management has already begun talks to extend Dro's contract. Dro turns 18 next January, and the board wants to settle his contract immediately. They intend to offer him a five-year contract extension.