Marouane Fellaini's first-half strike gave the visitors a deserved lead, but the Belgian then conceded a penalty for a challenge on Edin Dzeko and Carlos Tevez tucked away the spot-kick.
But City were unbale to breach Everton's discplined defence in the second half, and Mancini was not happy with the finishing of his front men.
"Everton is always a difficult game because they work hard, they defend very well," he said. "In the second half we played better, probably deserved to score another goal.
"In the end we are not happy but the season is long and this doesn't change anything. If you don't pay attention you can lose three points and it is sometimes better to take one.
"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 home crowd turned on Mancini when Aguero replaced Tevez rather than the ineffective Dzeko in the second half, but he added: "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."