England looked on course for a place in the final before conceding twice in the final 15 minutes, leaving Thomas Tuchel's side facing a third-place play-off against France.
Kane enjoyed an outstanding tournament, scoring six goals to become England's all-time leading World Cup goalscorer. The Bayern Munich striker will be 36 by the time the next World Cup is played, but he believes age alone should not decide when his international career ends.
"It's too early to talk about that," Kane said.
"As a person, it's always just about taking it year by year and how I feel.
"The national team is my pride and joy. It's what I love to do most, more than anything."
Kane pointed to Argentina captain Lionel Messi as proof that players can continue performing at the highest level well into their late thirties.
"Obviously, four years is a long way away. I'm 33 in the summer, but as you saw on the other end with Messi there, he's still performing at the highest level," he said.
"So, I never want to put a limit on these things.
"I'll address every situation as they come, but for now it's just about processing another tough loss with this team."
England must now regroup quickly before taking on France in Saturday's third-place play-off in Miami, with their UEFA Nations League campaign against World Cup finalists Spain beginning just over two months later.
Kane admitted the disappointment inside the England camp is difficult to put into words after seeing victory slip away so late in the match.
"There's not much to say for now," he said. "Everyone has to process what's just happened.
"Everyone's gutted. I'm gutted for all the boys, all the staff, everyone behind the scenes, because we know how much everyone puts into being a successful national team.
"And when you're so close, when you're 10-plus minutes away, and it slips out of your hands like that, obviously the lads are devastated.
"Now we just have to take it on the chin. There's nothing we can do. We go away and try to improve."
Slovenian referee Slavko Vincic has said he was overwhelmed with emotion after learning he had been chosen to officiate Sunday's 2026 FIFA World Cup final between Spain and Argentina at MetLife Stadium.
Anthony Gordon admitted England's heartbreaking World Cup semi-final defeat to Argentina will stay with him for some time, saying he believed the Three Lions were finally destined to end their decades-long wait for glory.
Youri Tielemans believes the time was right to join Manchester United, saying the club's ambition and desire to compete for major honours convinced him to make the move.
Barcelona president Joan Laporta has revealed that his club have made a big official offer for Atletico Madrid and Argentina forward Julian Alvarez this summer.
