“The other day I said this group never stops surprising me,” Scaloni said.
“And I’ll tell you the truth, we’re going to try to win, we’re going to leave everything out there.”
“But after this it’s very difficult to get people to understand what these players are showing. It’s incredible. We are unique, truly, and it’s not arrogance, it’s from the heart.”
Anthony Gordon fired England ahead in the 55th minute but Argentina refused to be beaten, pouring forward in waves and forcing their opponents back.
Enzo Fernandez smashed home an equalizer from Messi’s assist 30 minutes later but still they were not done.
Substitute Lautaro Martinez rose to head home Messi’s cross in stoppage time to complete the comeback and England ran out of time.
It is a bitter blow for the Three Lions, who have come so close at recent major tournaments but have been unable to get over the line.
Tuchel defended his tactics after England appeared to hand the initiative to Argentina.
“In the moment, no regrets. The team gave everything and we were very, very close,” the German said.
“We deserved to be up 1-0.”
“We played one of our better matches, maybe our best match in the circumstances. The team was top, we couldn’t get over the line but no regrets.”
Captain Harry Kane said the English disappointment was enormous, adding: “Gutted for the boys, gutted for everyone — the team, the staff, the fans.”
“God Save the King” was drowned out by Argentine singing in a crowd dominated by supporters in the blue-and-white shirts of the defending champions.
David and Victoria Beckham were in the crowd at the air-conditioned Mercedes-Benz Stadium, along with Rolling Stones frontman Mick Jagger.
England broke the deadlock 10 minutes into the second half when Gordon burst into the box, getting in front of Nahuel Molina to sidefoot home Morgan Rogers’ cross.
Scaloni made a triple change after the second-half hydration break as he searched for a way back into the game.
Alexis Mac Allister thundered a header against England goalkeeper Jordan Pickford’s right-hand post and then drew another save as England clung on to their slender lead.
Three-time champions Argentina got their reward in the 85th minute when Chelsea midfielder Fernandez lashed home from outside the penalty box after being set up by the irrepressible Messi.