The defending champions have played with fire throughout the knockout stages of the tournament and had to dig deep again on Wednesday (Thursday AEST), scoring two goals in the final 15 minutes to beat England 2-1 in the semi-final.
Their latest rally came after needing extra time to beat minnows Cape Verde and 10-man Switzerland, while also scoring three goals in the final 15 minutes to beat Egypt 3-2 in the last 16.
But they got the job done to set up a date with Spain on Sunday (5am Monday AEST) in New York, aiming to become the first team to win back-to-back World Cups since Brazil in 1958 and 1962.
"I'm speechless, it's a joy for the group, for our people, they never stop surprising me," Scaloni said.
"We're going to try to win, we're going to give it everything. But this is already impressive. We're unique and it's not arrogance, it's heart."
A game that looked like it would go down in English football folklore instead ended in all too familiar despair as the dream of football coming home for the first time since 1966 ended in Atlanta.
"I'm gutted. I'm gutted for the boys, I'm gutted for everyone, the team, the staff, the fans. We played a good game for the large majority of it, England captain Harry Kane told BBC Sport.
"Once we went 1-0 up we seemed to just try and hold on which at this level is just not enough, so I'm gutted."
Anthony Gordon's strike had England on the cusp of a first men's World Cup final since Sir Alf Ramsey's heroes lifted the trophy on home soil, but the reigning South American champions never quit.
Willed on by a febrile fanbase and the magic veteran star Messi, Argentina finally found a way past Thomas Tuchel's men when Enzo Fernandez slammed home five minutes from time.
Messi, 39, teed up the midfielder for that goal and swung over the added-time cross which striker Lautaro Martinez headed home to again break English hearts.
Having lost back-to-back European Championship finals under Sir Gareth Southgate, this was another case of so close yet so far for England.
Tuchel looked to have gone too defensive too early as, just like Croatia at this stage eight years ago, they threw away a chance to reach the final.
The Football Association's decision to hand him a two-year extension in February is sure to come into question in the following days, but asked if he believed he got his decisions wrong, the England boss said: "No, I believe that's just the nature of the game.
"As soon as you lose, you get criticised ... No one knows what would have happened if we made different decisions.
"I'm responsible for them, I took them, so I take the criticism. That's just the way it is.
"The World Cup is not over ... there is still a match to play, that we are not looking forward to so much, but there is still a match to play."
England's loss means they will face France in the third-placed play-off in Miami rather than playing for a shot at immortality against La Roja.
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