The result leaves the tie delicately poised ahead of next week’s return leg at the Etihad Stadium.
City are seeking revenge for their loss to Real at the same stage last season and Grealish feels the Premier League side’s home record gives them the edge.
The England midfielder told BT Sport: “We have a new team this year, different players.
“We’ve learned so much since last year. Now we have the perfect balance of experience and a few youngsters who are just world-class.
“I think we just have quality and I’ve never felt so confident going on to the pitch and having these players around me.
“Within ourselves at the Etihad, we feel unstoppable there. We came here to try and win, but it shows our character to go a goal down – it’s always difficult to play at a place like this.
“In the end I think it was a fair result. They had their chances, we had a few as well.”
— UEFA Champions League (@ChampionsLeague) May 9, 2023
City controlled a lot of the early play but Real soaked up pressure and hit them with a fine counter-attacking goal.
City manager Pep Guardiola praised his side for the way they fought back when under severe pressure.
Guardiola said: “It was a really tight game. Congratulations to the team because this team (Real) are always so difficult for their history and also their quality.
“We started really well and when we were better they made an incredible transition (and scored).
“When they were better than us in the second half, we scored. It’s open to Manchester, it will be a final for our people and we look forward to it.”
Real manager Carlo Ancelotti was booked amid commotion on the touchline as De Bruyne celebrated his 67th-minute equaliser.
The Italian revealed afterwards he had been complaining the ball went out of play in the build-up to the City goal. He also claimed he had seen proof he was correct.
Ancelotti said: “The ball was off the pitch. Technology said it and I don’t understand why VAR didn’t check it
“The referee didn’t pay attention to many things tonight.”
Ancelotti, however, was happy enough with his side’s performance and the state of the tie.
He said: “We have to play like this again next week. Our strategy was good, we weren’t worried when they had possession.
“Then the second half was completely different. We had the ball and created opportunities. We are very satisfied. “