City came from behind to win 2-1 in Madrid on Wednesday to move up to fourth in the Champions League table.
Away from Europe, Pep Guardiola's side are trying to chase down Arsenal at the top of the Premier League.
And Gvardiol believes it's a good sign ahead of the second half of the campaign that City have proved they are capable of delivering big results when it matters most.
"I agree with you," said Gvardiol when asked whether winning in Madrid is evidence that City can beat anyone this season.
"I mean, obviously, we know how difficult it is to play here, and we've seen so many games, so many teams struggle to play here.
"But it's not the first time that we play here. Of course, we analyse them [Real Madrid] at the moment, maybe they are not in really good form.
"So we took an opportunity for an important three points for us to fight for top eight in the Champions League.
"I think we need to recover, well. Obviously, everyone is tired mentally and physically as well. Crystal Palace on Sunday, we need to prepare well and hopefully we go there and have a good game."
After back-to-back defeats to Newcastle and Bayer Leverkusen, City have won four games in a row scoring 13 goals in the process.
Guardiola's teams have a history of putting together long winning runs at the business end of the season.
And despite losing lots of experience following the departures of Éderson, Kyle Walker, Ilkay Gündogan and Kevin De Bruyne, Gvardiol insists the new-look squad can still do it.
"I think so," he said.
"I think we're doing good. Like I say every time, we go game by game, not to look too far ahead.
"And we have a good team, obviously. We have amazing players on the bench, who are more than ready to come in. So I think we have a good team and we want a fight."
After starting his City career at left-back, Gvardiol has moved into the centre to partner Rúben Dias in the middle of defence.
The move has been partly motivated by Nico O'Reilly's form at left-back.
The 20-year-old scored the equaliser against Real Madrid to continue an impressive season which could yet end with an appearance against Gvardiol's Croatia at the World Cup next summer if he can earn a place in Thomas Tuchel's England squad.
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"I'm super proud of him," said Gvardiol.
"I'm really happy for him as well. He's young, but to be honest with you, two days ago I was thinking that when I see him playing next to me, I feel like he's 30. I think he has a quality.
"There's a reason he's in the starting XI. He just needs to keep going. He has the full support from me, from everyone in the team, from the manager, staff as well, from the club. He can do such big things in his career."
