Mancini admitted his team struggled against a side who they have beaten only once in 14 trips to Goodison Park.
"Everton at home is a strong team," he added. "Every time they play against us they play very well.
"This evening we had the chance and when we conceded a goal we didn't have more chances to score."
Darron Gibson revels in 'unbelievable' result for Everton
Other than a couple of Samir Nasri efforts which hit the bar, City were restricted to two penalty appeals, first when Sergio Aguero was brought down and then when Aleksandar Kolarov's cross appeared to strike Phil Neville's arm.
"The decisions are very unlucky against us at this moment," said Mancini, who has also had to do without the suspended Mario Balotelli.
"It's very important that we start to win next Saturday against Fulham. The season is long, we have 15 games [to go] and I hope we can recover all the players quickly.
"But it's important that we recover our strength this week."
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