Cherki struck inside the final ten minutes to settle the game 2-1 win City's favour.
The France midfielder said afterwards: "We knew coming to Nottingham, it was very complicated because Forest is a very good team. We are very proud to win the game.
"I know my qualities. I gave a good pass for Tijjani Reijnders and it was a very good finish. I'm very proud of the team because today is a big win.
"When you come here, you know the team of Nottingham Forest is a big team with a lot of good players. I'm very proud to score for my team because the season is so long and we need all the points."
On scoring his second Premier League goal for City, he added: "All the time I want to score goals, but it is not my role. Erling is here for that! I want to give my team-mates a good pass and I am very proud of that."