Mancini did not expect Kompany's calf problem to cause such a lengthy lay-off and he describes the 26-year-old's absence as "a big problem".
He said: "Probably we made a mistake because when we knew [of] this problem we were four days to [the] close [of] the market. Probably then we should maybe have bought another defender.
"Also, last year he had this problem - for one month he didn't play. This is a big problem. For me we did a mistake in this case.
"We had a chance because we had one good defender, but we didn't think that Vinny would stay out for 40-45 days."
Kompany will not feature in this weekend's match at Everton, but he could return when City host Newcastle United on March 30.