The champions face the Black Cats at the Stadium of Light on Boxing Day with the Italian revealing that the England international had grown frustrated with his lack of first-team opportunities at City.
"I didn't say to him to leave. Adam said he wanted to always play and for that reason I let him go," Mancini told reporters.
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However, Mancini says Johnson was a valued member of the City squad but appreciates his reasons for wanting to leave Etihad Stadium.
"For me Adam was an important player but I understand the situation," Mancini continued.
"He is young, he wants to play every game."
Mancini's side are second in the league heading into the Boxing Day fixtures, four points behind leaders Manchester United having gained two points on them after their rivals' 1-1 draw at Swansea on Sunday.