Dembele sealed a scintillating performance with his third goal in six games as Barca beat 10-man La Real 1-0 to book their place in the semifinal.
In addition to his goal, Dembele caused the away side problems throughout the game with his pace and created a great chance for Gavi, who hit the crossbar.
"I think Dembele has matured a lot since we took over," Xavi said in a post-game news conference. "We have just given him the tools. He is lethal. We always say when he comes inside, he has to shoot more because he has that quality and he can make the difference in games.
"You see the faces of the full-backs, they suffer. We have just given him confidence. He has so much potential. I believe in him. I think a lot of this comes down to making the right decisions. He is also enjoying himself and the fans are enjoying him."
Dembele's moment of form -- he now has eight goals this season -- contrasts with the situation he was in one year ago, when Barca dropped him from the squad due to a stalemate over a new contract.
The former Borussia Dortmund winger eventually signed a new two-year deal with the club and is now one of the most important players in Xavi's side.
"I am delighted for him because he is a good guy and a good professional," Xavi added. "He has turned things around and that is not easy at Barca.
"He's the one full of confidence and quality. We try to guide him. For me, he is one of the best in the world in his position.
"He has so much quality, but from there you have to believe in yourself. At Barca, it's important to have that mentality to believe that you can influence games."
Visiting coach Imanol Alguacil agreed that Dembele was the difference between the teams and suggested his players faced him with fear.
"It's hard to stop a player at Dembele's level, with the form he is in at the moment," Alguacil said. "He can breeze past two or three players in five meters if you give him space.
"That said, we made it too easy for him in the first half. I think we were scared of him. And if you give Dembele half a yard, you're screwed."
Barca dominated the first 30 minutes and eventually took the lead early in the second period after Brais Mendez had been sent off for the away side.
However, La Real, despite being a man down, fought back late on and had chances to equalise. Alexander Sorloth missed when it was easier to score from six yards and Barca goalkeeper Marc-Andre ter Stegen made two late saves.
"We are annoyed because we wanted to get through," Alguacil added. "It's difficult here 11 vs. 11 against Barca in their current form, so imagine... But we knew we would get chances. We were close, even with a man less.
"I don't usually like the word proud because it means you have lost and we came to win. But against Barca, in their form, with 10 men and [against] a player like Dembele, it is complicated. In the last 10 minutes, they seemed more nervous and 1-1 seemed more likely than 2-0. But it still hurts."
Xavi, meanwhile, was happy with Barca's performance, but not the way they took their foot off the gas and failed to put the game to bed.
"The majority of things are positive, but you can't relax after the goal," Xavi said. "I would say for an hour we were brilliant. We dominated 11 vs. 11 and created a lot of chances to score. They had one chance with 11, Take Kubo off the bar.
"The sensation is that we complicate things when we don't kill games off. We have to be more clinical. There have been times when the defence or Ter Stegen have had to save us. There are lessons to learn, but that's football.
"We are where we want to be, three points clear in the league, in the semifinal of the Copa and with a trophy, the Supercopa, in the bag."