A stunning strike from Kevin Mirallas put Everton in front, but Christian Eriksen levelled before a rare goal from Roberto Soldado gave Tottenham a lead they kept to the final whistle.
“I think we can do better in possession, but I think we showed character,” Vertonghen said. “We had a very good defensive line, the midfield and strikers as well were very good. It was a team performance today.”
Harry Kane had a hand in both goals, winning the ball from Gareth Barry to set up Soldado’s strike as Tottenham put pressure on Everton throughout.
“It helps that the strikers and midfielders press their direct opponents because it makes the distances smaller,” Vertonghen added. “It makes our job easier.”
Kane missed out on a goal of his own but was named man of the match.
“It feels good to get the win because it was tough out there,” he said. “Everton are a great side and it was a good battle between both teams. I’m absolutely buzzing to come away a winner.
“We’ve been working on pressing higher up the pitch and creating opportunities. Obviously I caught (Barry) on the ball. It’s good to see what the manager has been working on working out on the pitch.”
Kane tangled with Muhamed Besic in the area and went over late on, but there was no penalty awarded.
“I think it was 50-50,” he said. “Sometimes you get them, sometimes you don’t. It was a tangle of legs and it made me go down but sometimes late in the game the refs don’t give them. But we got the win in the end so it doesn’t matter.”
Everton manager Roberto Martinez was left frustrated, claiming his side’s performance was worthy of a better result.
“It was one of those performances where it’s really difficult to take the result at the end because it’s very harsh,” he said. “We performed really well.
“Remember we are playing away from home facing a team with a lot of individual quality but once we scored that first goal, the hardest moment of the game, for five or 10 minutes after we couldn’t impose ourselves and take the game away.
“I did feel that was the moment where we could really make a mark in the game but then we were little bit sloppy. Their two goals were very fortunate breaks.”
Martinez felt that luck was not on his team’s side, and claimed Everton should have had a penalty after Romelu Lukaku’s header struck the arm of Federico Fazio.
“His arm is not in a natural position,” Martinez said. “But you feel it’s a day where none of the breaks you need went in our favour to get a positive result.”
Opposite number Mauricio Pochettino could be much happier both with the result and the commitment shown by his players to his pressing style.
“Today was a very important victory,” he said. “I think that always you need time to set out your philosophy but today we can be very pleased.
“(Coming from behind) is important. It shows we have character, personality, we are brave. It was very difficult because with their first shot they score and afterwards it’s never easy but we were very aggressive in our game and we showed our style.
“We need to keep this mentality and try to show this in the next game.”
TOTTENHAM HOTSPUR: Lloris, Chiriches (Dier 70), Fazio, Vertonghen, Davies, Mason, Bentaleb, Lennon (Lamela 61), Kane, Eriksen, Soldado (Paulinho 81).
EVERTON: Howard, Coleman, Jagielka, Distin, Baines, Besic, Barry, Mirallas (McGeady 61), Eto’o (Osman 61), Barkley, Lukaku.