Anthony Gordon's strike had put the Three Lions on the cusp of a first men's World Cup final since they lifted the 1966 trophy, but Lionel Messi inspired a dramatic turnaround in Atlanta.
He set up Enzo Fernandez, who blasted home from outside the area, and provided an inch-perfect cross for Lautaro Martinez's winner in stoppage time.
"Gutted for the boys, gutted for everyone - the team, the staff, the fans," England captain Kane told the BBC.
"We played a good game, the large majority of it. When we went 1-0 up we seemed to try and hold on, which at this level is not enough.
"So, just gutted because we've worked so hard to be here and the lads have given every last bit of running, blood, sweat, tears."
Bayern Munich forward Kane, who scored six goals during the tournament, said Thomas Tuchel's men had struggled to repel constant attacks from the defending champions.
"After the goal, whether it was them putting more men forward or us not being able to match them man for man, it was just wave after wave," he said.
"Lads were putting blocks in but, in the end, it just wasn't enough."
He said England had not planned to rely on defending after Gordon's goal.
"When we went ahead the messaging was to go again and get another goal," he added.
"Then once they scored their two goals it was to try and find something but we couldn't quite get the momentum back in the game."
World Cup 2026
The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
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