The Belgian has managed just 15 Premier League appearances for the defending champions this season, while Manchester United have opened up a 12-point lead at the top of the table
Kompany has not featured for the champions since January 26 and has only made 15 appearances in the Premier League this season.
"Probably we made a mistake," Mancini told reporters. "We knew the problem [with Kompany] and we were four days to the close of the market. We probably should have bought another defender - we tried.
"But we didn’t think that Vinnie would be out for 45 days. Vinnie has started to run, and we hope and think he’ll be ready for [the game against] Newcastle.
"He [Kompany] started training with us four days ago, but he was tired because he worked a lot. His calf was tired, but it is no problem. We don’t want to take a risk at the moment.
"We have one game then the international break, better that we wait. I don’t think he is out for the season but the calf is a dangerous injury. If you don’t recover well, you can have a problem for four, five, six weeks in a row. After the break, I think he will come back."
The Italian is hoping that leaders Manchester United will drop points between now and the Manchester derby on April 6 as City look to upset the odds and stage a stunning comeback into the title race for a second consecutive season.
"United play at home against Reading and then go to Sunderland," said Mancini.
"We hope we can play the derby with a gap of nine or seven points, certainly less than 12. Because from the derby to the end of the season, United have three or four difficult games."