The Uruguay midfielder signed a new long-term contract with Spurs last month.
He told the club's website: "We have a new manager (Thomas Frank), and the new captain is my friend, Cuti (Romero). He deserves this, to be captain in this Club. I enjoy this also.
"My teammates and every person here is amazing. Every player. I enjoy every day in this Club because of them. My teammates are amazing. So I’m very happy.
"We want to win another trophy this season. This is the most important thing. I want to continue at this level, I think I feel every day getting better and better, so I want to continue in this. And I want to win more trophies for this Club."
On winning the Europa League title last season, Bentancur added: "After we won in Europe, it was fantastic. We worked hard every day for this, and now we want to continue. I’m very happy and, as I told you before, I want to enjoy this moment and enjoy more years at this Club.
"It’s fantastic when you win trophies, also after long years in this Club, don’t win another trophy. When you win something important, it’s huge for the players. I’m very happy and I want to continue to win trophies.
"We celebrated in the hotel with the team. But then, when I took my holidays, we celebrated with my whole family and my wife’s family. It was good, very good. When you win something, you can celebrate with your family too, and that’s very important."