On Bergvall, De Zerbi said Spurs need to “help him improve” and he was “fantastic” at the beginning of pre-season.
“It is difficult because of the competition in his position,” he said.
“[Sandro] Tonali, [Rodrigo] Bentancur and [Conor] Gallagher are all a high level, but at the end of the season he will play a part in many games, I think, and then he has to improve.”
So far this season, he has played 45 minutes for Spurs in the Premier League.
“I think we’re building something great here. It’s an exciting time for the club and that’s why I’m happy to extend my contract,” Bergvall said.
“I’m always trying to achieve as much as possible, to be the best version of myself both on and off the pitch and I know this is the right place to do that.
“Personally, my goal is to produce more for the team – performances, goals and assists – to help as much as I can. I’m getting better every day in training and I’m looking forward to what will be a really good season ahead.”
De Zerbi said in July Bergvall, was “a top, top, top player” but made clear he would not try to “convince anyone to stay” against their wishes.
The Italian admitted he had made mistakes in his handling of the player during a chaotic end to last season, in which Spurs narrowly avoided relegation.
Speaking about Bergvall’s renewal, De Zerbi said: “I believe his best football is still ahead of him and we want to give Lucas the platform to reach his full potential.”