The Blaugrana secured a comfortable 4-0 win at Camp Nou on Saturday through penalties from Andres Iniesta and Cesc Fabregas complemented by strikes from Alexis Sanchez and Pedro, with 17-year-old Traore replacing Neymar in the 83rd minute to make his first senior appearance.
Speaking after the game, Zubizarreta claimed that the introduction of Traore underlines the Barcelona trainer's in-depth understanding of the club and its emphasis on youth development.
"Tata has understood what we are as a club and that when there are injuries, we turn to the younger players," the 52-year-old told journalists after the game.
"Adama is very young, but one thing is that he has been brought up here. Let's not forget that we also had [Martin] Montoya, [Marc] Bartra, Sergi Roberto. This is the new generation with whom we can continue dreaming."
Local-born forward Traore is a Spain Under-19 international and had played only four times for Barcelona B before making his senior bow.
Zubizarreta also praised the performance of goalkeeper Jose Pinto, who stood in for the injured Victor Valdes on Saturday.
"[Pinto] knows what it is to play for this shirt," the former shot-stopper continued.
"He dominates his area and has been strong when needed. He was very good, he gives us peace of mind and demonstrates that he is here because he is at that level required."
Barcelona sit top of La Liga with 40 points from 14 games, three ahead of Atletico Madrid in second.
