It was the third consecutive loss Enzo Maresca’s men have suffered.
The hosts began the match in brilliant fashion, scoring twice within the opening 20 minutes.
Jair Cunha pounced on a defensive error to make it 1-0, before Liam Delap raced through to finish high into the net.
At the start of the second half, City threatened to stage a comeback, after Rayan Cherki produced a stunning finish.
But Delap added a third for Forest from a swift counter-attack.
