Kane finished top scorer in the Barclays Premier League last season with 25 goals but failed to carry that form into Euro 2016, where he was one of England’s most disappointing performers.
The 22-year-old was taken off at half-time in England’s second game against Wales and criticised for botching a series of set-pieces while struggling to offer a serious goal-threat.
Kane was also under pressure 12 months ago, following a brilliant breakthrough campaign, and former Spurs skipper King expects a similar response this time around.
“I’m entirely confident in Harry getting back to his best,” King told Press Association Sport.
“He’s the kind of player who doesn’t seem to suffer from a lack of confidence, he always has the utmost confidence in his ability to score goals.
“It wasn’t a tournament where he was missing lots of chances, he just wasn’t able to find the positions that he normally does.
“I’ve got no worries for Harry, he’ll be back, he’ll be hungrier as a result and he’ll be looking to prove people wrong again.
“He did that last season when people were asking if he was going to be a one-off and he can do it again.”
Kane was not the only Tottenham player to suffer England’s miserable exit, with Dele Alli, Eric Dier, Kyle Walker and Danny Rose all on the field for the embarrassing defeat to Iceland.
Mauricio Pochettino’s first job will be to revive his players’ spirits, as Spurs bid to balance a renewed title challenge with the added test of Champions League football.
“You expect criticism as a top player and even more so as a young player as well,” King said.
“When you’re young you’re going to have games and spells where you’re not scoring or playing so well. When you’re young people question your ability more.
“The whole squad received criticism and that’s what you expect, especially when you play for England. The players are used to that.
“I don’t think they listen to it too much. It’s all about how they feel themselves. When you do receive criticism, it motivates you to come back stronger.”
Kane may yet be eased into pre-season more gradually than his fellow internationals, which could give new signing Vincent Janssen an early chance to impress.
Janssen’s £17million move from AZ Alkmaar was confirmed on Tuesday, the young Dutchman following midfielder Victor Wanyama as Tottenham’s second signing of the summer.
“I’m pleased with those two signings,” King said. “Another attacking option was very important and Janssen has a great scoring record from playing in Holland.
“Wanyama I’ve seen many times and I’ve been very impressed by him. He’s a bit like Eric Dier, you don’t see all the good work he does.