The injured Belgium international has not featured for the defending Premier League champions since their 1-0 victory over Stoke City in the FA Cup on 26 January.
Kompany has been nursing a calf problem, leaving the Citizens short at the back, with England international Micah Richards also sidelined due to a knee injury.
Mancini concedes that City never anticipated Kompany would be unavailable for selection for almost two months and opted against bringing in a replacement.
“We made a mistake. We knew the problem and we were four days to the close of the market,” Mancini told the Telegraph.
“Probably there, we should have bought another defender. We tried. We had a chance, but we didn’t think Vinny would stay out for 45 days. This was the big problem.
“Also, last year, he had this problem for a month and didn’t play.”
With City trailing Manchester United by 12 points in the Premier League title race, Mancini is desperate to restore his skipper to the Citizens’s starting line-up.
And the Italian hopes to have the Belgian defender back for City’s clash against Newcastle United on 30 March ahead of their trip to Old Trafford in early April.
“Vinny has started to run. We hope and think he will be ready for Newcastle [on March 30],” added Mancini.
“He started training with us four days ago. 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, so it is better that we wait.”
MORE: The latest football news