Players were in tears after Rodri's emphatic second-half goal against Inter Milan in the final secured a 1-0 victory and City's first Champions League title on Saturday, having wrapped up the Premier League and FA Cup last month.
"Unbelievable. Difficult to put anything in words. Today, we made history," Gundogan told BT Sport. "This team deserves the highest recognition and winning the Champions League elevates us to the very top of the game.
"We knew everyone was talking about the treble. The pressure was there, but this team is built to handle the pressure in the best possible way."
Grealish, who joined City from Aston Villa for a British record 100 million pounds ($126 million) in 2021, has been one of City's standout performers this season and was overcome with emotion at the final whistle.
"This is what you work your whole life for. I'm just so happy," Grealish said. "I was awful today but I don't care.
"I've just said to (Guardiola): 'I want to thank you because you've made this happen for me. You put so much faith in me, buying me for a lot of money.' Even last year when I was playing crap he stayed there with me and this year he's given me that platform ... He's just a genius."
Striker Erling Haaland has already set his sights on more success next season, warning rivals that a treble has not satisfied his appetite for trophies after spearheading City's attack with 52 goals this season.
"In my wildest dreams I would never think of this," Haaland said. "After a couple of days when this settles a bit and this feeling of winning this trophy, I will want to do it again for sure.
"We have to defend what we have achieved this season. That's how it works. In a month everything is forgotten and we have to start again."
City got the job done without chief playmaker Kevin De Bruyne, who was consoled by Haaland and his team mates when he was forced off with a hamstring injury in the first half.
"It's what I've been fighting for for many, many years," De Bruyne told reporters. "It's incredible we've been able to achieve that with City.
"It's the first one in the history of the club. We'll always be associated with the club in that way. It's really special."
