Tuchel's side were pegged back to 2-2 at the interval in their Group L opener in Dallas on Wednesday (Thursday AEST) after two Kane strikes were cancelled out by Martin Baturina and Petar Musa.
England raised the tempo after the break and won in commanding style after goals from Jude Bellingham and Marcus Rashford.
"I thought first half we were OK, but really disappointed to concede the way we did, the way we dropped off," England captain Kane told ITV.
"Credit to the manager ... gave us a speech at halftime just to say if we lose we lose, but we lose in our way.
"You saw that the way we came out in the second half, we came out full gas. They couldn't live with it and that's the level we have to set every game.
"The first game of the tournament. A great result against a tough side."
Real Madrid midfielder Jude Bellingham added: "It wasn't one of those where there was a big drama – he (Tuchel) wasn't standing up shouting. It was just what the team needed.
"We have a mature group, we have great leaders in there. Everyone knew the level we had to get to and why we weren't hitting it. We were very clear in the second half and the early goal gave us the platform."
England now play Ghana next Tuesday before facing Panama in their final group game a week on Saturday.
"We were too focused on the result, too focused on protecting the lead which we didn't have (any more)," German Tuchel said.
"I loved the reaction of the players in the second half. We deserved to win, but it was emotional."
Kane came into the tournament on the back of a record-breaking season in Germany and equalled Gary Lineker's record of 10 World Cup goals for England.
The Bayern Munich striker won the 2018 Golden Boot in Russia when he scored six goals during England's run to the semi-finals, including a hat-trick against Panama.
He then bagged another two during the Qatar edition, but missed a penalty against France in the quarter-final defeat.
Lineker scored his 10 goals in two tournaments, winning the 1986 Golden Boot with six in Mexico before adding four at Italia '90.
But with Kane on the board so early, he will be hoping to become the first player to win two Golden Boots and matched rivals Kylian Mbappe and Erling Haaland, who both scored braces in their opening matches.
The Texas encounter was one of the games of the group stage, with 70,389 watching Tuchel mastermind a first win against a team in FIFA's top 20.
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