The champions could only come away with a point in a 1-1 draw against Steven Cooper's side.
Bernardo Silva gave the hosts the lead at the City Ground only for Chris Wood to salvage a point for Forest in the second half.
City's draw, coupled with Arsenal's 4-2 win at Aston Villa earlier in the day, handed the initiative back to the Gunners, who hold a two-point lead at the top of the table with a game in hand.
"Congratulations to Nottingham for the point that they got," the City boss said.
"It was a brilliant performance, we played really good but we didn't score. We have to score and we didn't do it and that's why we dropped points.
"For the goal we could defend better, more energy but the way we played was brilliant.
"In the first half, it should be already be two- or three-zero, we conceded one shot on target and we dropped points.
"It's sad and disappointing but the way we played was really good."
After the morale-boosting win over Arsenal in midweek, Man City defender Kyle Walker thinks it is unacceptable for two points to be dropped in such a manner.
"First and foremost, we go to the Emirates [where they beat Arsenal in midweek] and play the game we did and then come here, it [the performance] is unacceptable," he said.
"If we want to compete with teams near the top, we need to win. We missed a few chances and we need to do better as a team.
"Sometimes it's football and sometimes it's emotion. Every game should be treated the same, like a cup final. What can I say other than it is unacceptable. We have to stick together as a group.
"The senior members of the team need to put our thoughts across. That is just not acceptable. We have to give credit to Nottingham Forest. They dug in and hung on. We have to do better."
