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Messi finally won the biggest prize of them all in Qatar last year, guiding Argentina to its first FIFA World Cup title since 1986.
Argentina appeared to be cruising to victory when 2-0 up at half-time, but a quick-fire double from Mbappe near the end of the regulation 90 minutes took the game to extra-time.
Messi's second goal of the game had Argentina back in control again, but as before, Mbappe levelled to complete his hat-trick with two minutes left, forcing a penalty shootout.
Argentina ultimately prevailed 4-2 on penalties to spark wild celebrations, some of which bizarrely seemed to revolve around Mbappe.
Goalkeeper Emiliano Martinez was said to have called for a moment of silence for Mbappe in the changing room afterwards, and then during Argentina's celebratory parade in Buenos Aires he was spotted carrying a doll with the PSG forward's face stuck on.
But Messi does not believe any of the controversy has impacted his relationship with his club-mate.
He said: "We talked about the game, the festivities, how people experienced it in Argentina when I was on vacation, and the festivities we had. Nothing, nothing more.
"I was on the other side too, I lost a [FIFA] World Cup final too, and I didn't want to know anything about it, about what happened, and nothing related to the [FIFA] World Cup at that time.
"That's why I don't want to talk about it [to Mbappe] either, but the truth is that there is no problem with Kylian, on the contrary."
Some of Argentina's celebrations – most notably Martinez's behaviour – fed into a negative perception of the team in the eyes of some.
There was also the photo of its reaction to beating Netherlands on penalties earlier in the tournament, with many of the Argentina players appearing to goad their opponents as they ran off to celebrate.
But Messi is adamant Argentina has been done a disservice, again explaining how its reaction to the Oranje was simply a response to apparent unsporting conduct from Louis van Gaal's team.
"It seems unfair to me that Argentina's lack of fair play was mentioned because it's not true," he continued.
"We always behaved in an exemplary manner, on and off the pitch. My team-mates were impressive.
"I think they talk because of what happened with the Netherlands, that it all started there. It was the Dutch who spoke and who wanted to destabilise our players when we were going to take the penalties.
"Everyone talks about what Argentina did after their victory but no one talks about that. It seems to me we should watch it back more carefully and see what happened, and then comment."