Fati scored twice and fellow youngster Pedri came off the bench late on.
"His performance has to be highlighted," Koeman said when asked about Fati's night's work.
"I'm very happy with him. We know he's only 17 and has things to improve.
"He has to find consistency and sometimes he lacks concentration.
"He wasn't so good against Elche but today he was. He had a great match.
"I'm very happy with him and Pedri. They both have great futures."
Antoine Griezmann started the night on the right of the three behind Fati, and Koeman was pleased with what the Frenchman showed.
"He can change positions with Leo [Messi]," Koeman said.
"It's more difficult for the opposition.
"I'm happy with his performance."