The Three Lions went ahead through Anthony Gordon before retreating into their own half, allowing the reigning champions to seize control as Enzo Fernandez and Lautaro Martinez completed the comeback.
Reflecting on the loss, Kane admitted England's inability to protect leads at major tournaments has become a recurring problem, saying his side ultimately paid the price for surrendering the initiative.
"A similar story to what has happened in previous tournaments. I feel like we struggle to keep the momentum of the game. We've done so well for 60 minutes; we scored, and we deserved to be ahead," said Kane.
"And then, for one reason or another, we struggled to keep the ball; we struggled to put pressure on the ball, and it just allowed them to create more momentum. It created more attacks for them in our final third."
"It's just a normal mindset to try and hang on to the one-goal lead, but with 20 minutes plus stoppage time to go, it was always going to be a long time. We are going to have to watch the game back and find out exactly how we can improve in those situations, but it's been probably the missing piece in the last four or five tournaments."
Kane refused to blame the tactics, however, only suggesting that whatever plan was implemented after taking the lead simply did not pay off.
The striker said there were not a lot of words in the dressing room afterwards.
"I don't think there's much to say. For now, everyone has to process what has just happened. Everyone's gutted and feels for all the boys, all the staff, and everyone behind the scenes because we know how much effort everyone puts in to be part of a successful national team."
"And when you're so close, when you're ten minutes away and it slips out of your hand like that, yeah, obviously, the lads are devastated. For now, we just have to take it on the chin; there's nothing we can do. We can congratulate Argentina, and yeah, we go away and try to improve."
Kane also delivered a message to the England supporters.
"Yeah, big thanks to the fans who have traveled. We know how much people have given up to be here and support us and how much it has cost and all those situations. Every game we have had, the support has been incredible. I know back home the fans have been totally behind us."
"Yeah, we are devastated for them as well. We know how much it meant to them; we know how much it would have meant to reach the final and have that day together. Look, we gave it everything, every last bit of blood, sweat, and tears. We tried to get into that final and give our fans something to cheer about , but in the end, we fell short."