Kane made his return from a two-month injury layoff to start Saturday's final in Madrid, but looked well short of match fitness in a disappointing Spurs display.
Dele Alli, Danny Rose and Eric Dier also featured for Mauricio Pochettino's men, while Liverpool trio Jordan Henderson, Trent Alexander-Arnold and Joe Gomez are included in Gareth Southgate's 23-man squad.
"You don't have to talk to people about switching off from club football," said Kane.
"Everyone just naturally does it and I think the fact we've played with each other in club sides and younger England sides (means) we're all good friends.
"Whether you're at Spurs or (Manchester) City or Liverpool, we've known each other long enough that we've become mates.
"When you come here, you just look forward to meeting up and being friends."
England have the chance to win a first tournament since 1966 at the inaugural Nations League, as they face a resurgent Netherlands in the second semi-final on Thursday.
Kane believes it is important for England to claim silverware as a building block towards next year's European Championship.
"It's a new tournament, but it's still a chance to win a trophy in an England shirt, and 1966 was a long time ago," Kane said.
"I think if we go on and win, it will be another stepping stone to go on to achieve big things in the future.
"Winning trophies breeds that mentality to go on to do more and more, so it's a chance for us to start early and try to achieve that."