It needed a Carlos Tevez penalty just before halftime to earn champions City a 1-1 draw and maintain their unbeaten start to the Premier League season.
"We spent most of the second half in Everton's half but we couldn't find a way through," Mancini told the club's website.
"Our strikers aren't firing on all cylinders at the moment and not scoring enough goals but they worked hard today and they will have periods like that during the season," added the Italian whose team are now unbeaten in 37 home league games.
"We are not going to go through the season winning every game and sometimes you have to accept it is not going your way and take something out of the game."
The manager started the match with Edin Dzeko and Tevez up front before trying substitute Sergio Aguero and Dzeko and ending it with Mario Balotelli, who came on in the 80th minute, and Aguero together.
"I took Carlos off because I thought Dzeko might get us another goal - I have my reasons for making the change but that takes nothing away from Carlos who played very well," said Mancini whose side have struggled to emulate their free-scoring of last season.
"Everton is always a difficult game because they work hard and are well organised. When we fell behind we had to take risks to get back in the game."
The visitors took the lead through Marouane Fellaini after 33 minutes. City were level before the break although Everton manager David Moyes was unhappy with the penalty, awarded for a foul on Dzeko.
"It wasn't a penalty - it appeared really harsh to me and it was never a foul," Moyes said.
"I'm not sure how many penalties City have had lately but the fact is we drew against the champions away from home and that's a good draw."
