Carlos Tevez, Sergio Aguero, Mario Balotelli and Edin Dzeko have scored just three goals in their last eight games, including a blank in the 1-0 loss to Sunderland on Boxing Day.
City have been linked with, among other strikers, a move for Atletico Madrid's Falcao in the transfer window but Mancini is distancing himself from any bids this January and is confident he can get goals out of his players – even if it means playing without a recognised forward.
Mancini told Manchester Evening News: "We can't keep thinking of bringing players in. We have a good team, good strikers, but we need them to be strong when they get a chance.
"We still have a big problem that we don't score, and we need to change. Maybe we need to play without a striker, or with just one striker. We need to do something. If we want to win this championship we need to score like we did last year.
"We have top strikers, but maybe we are too soft when we get a chance because we think we have good players and maybe we feel we will score the next chance that comes along.
"We have four top strikers, and it is time that those top strikers started to score. That is what they are there for, to score goals."