Although Carlos Tevez got on the scoresheet, Mancini remains frustrated with the goal output of his strikers.
He said: "In this moment we are not very strong with our strikers. We need them to score more goals.
"They are four top strikers but this can happen during the season.
"It is important they work hard like they worked today. Dzeko, Tevez, Sergio (Aguero), Mario (Balotelli) - in this moment we are like this but I think we will solve this problem."
The crowd booed when Mancini opted to replace Tevez with Aguero in the second half, rather than taking off Edin Dzeko, who endured a frustrating afternoon.
Mancini said: "I have my reason for this. I am not stupid. I understand the supporters.
"For the supporters, if I put on four strikers and take off four defenders, they are happy. But football is not (like) this.
"Everton can score only on set-pieces. I needed one or two players that could also help the defenders in this situation.
"I also thought that Dzeko could score one goal in that moment, not because Carlo played worse than Dzeko. Carlo played very well."