Leading 2-0, Barca had Marc Casado sent off before conceding twice inside the final 10 minutes.
An unhappy Gavi rapped afterwards: "We were in control of the game, but the sending off affected us a lot. They scored against us in two specific actions. We can't have a player sent off, because then this happens.
"The first goal was a stupidity. We had to clear the ball. It's football and we have to learn. And with one man less it's difficult to get the three points.
"Was I asking my teammates to calm down? If you stop concentrating, whatever happens happens."
Finally, on his return as a starter, Gavi added: "I'm happy, it was after a year. The important thing was the three points."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play