Carlos Tevez and Sergio Aguero again failed to find the back of the net against Sunderland on Boxing Day as City suffered a surprise 1-0 defeat.
Mancini's attacking force, which also consists of Mario Balotelli and Edin Dzeko, have only scored three goals between them in City's last eight matches.
The manager is not ruling out playing one striker up front or even none at all if his frontmen do not start scoring.
But he is not planning to bring more players in to bolster his already star-studded squad, despite City being linked with Atletico Madrid's prolific striker Falcao.
Mancini told the Manchester Evening News: "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."
He added of the transfer speculation surrounding City: "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."