Spurs secured a 2-0 victory in their first game at the Tottenham Hotspur Stadium on Wednesday night, but that was their first win in five Premier League outings after two defeats and two draws in their last four.
City, on the other hand, have been in scintillating form of late, with even Liverpool boss Jurgen Klopp saying they look like the best team in the world and can win the Quadruple this season.
"In football, you never know," Son said after Spurs' victory over Palace. "Who could imagine that we would have such a hard time for the last five games?
"The Man City game will be played at our home, it's a Champions League game. I believe if we can do what we always do, we can make a good result."
The South Korea international made history when he scored the first goal at Tottenham's new stadium with a 55th-minute strike on Wednesday.
It was a memorable night for the north London club, and Son continued: "I really like Tottenham a lot. I just wanted to win, this is the crucial part!
"I thank everybody who helped me [in scoring the goal]. Tottenham, team-mates, coaching staff, the fans, everyone. I didn't score [the first goal] just because I was good enough, I think I was just lucky.
"I played in a lot of stadiums. In the Bundesliga, in Champions League matches as well. But, I feel honoured to play in such a nice stadium. It's magnificent. I hope we can show good performances in such a great stadium."
Asked whether he had made it a target to score the first goal at the new stadium, Son added: "No, I didn't. I really like Tottenham, a lot. My time here has brought me so many things. I just wanted to win.
"It was a historic game, and we didn't want to show a poor performance. I focused on winning, and I believe today's win will help us for the rest of the season."