Sergio Aguero struck twice to give City a healthy lead but Fulham drew level following a goal by Bobby Zamora and Danny Murphy's deflected shot.
The result was the first time City have dropped league points this season.
Mancini told BBC Sport: "It's incredible, we lost two points after we scored two goals and dominated the game.
"But I think this can be a lesson for us. When we have the chances we should score."
Mancini complained of his team's wastefulness after the 3-0 win against Wigan last Saturday, where they had a host of chances but only led 1-0 at the break.
This time, although Aguero scored within 12 seconds of the re-start to give City a two-goal cushion, they were made to pay.
Fulham 'kept believing' - Jol
It was the first time City have played a game after a Champions League fixture but, while they faced Napoli at home on Wednesday, Fulham had played a day later in midweek, hosting FC Twente in the Europa League on Thursday.
Mancini bemoaned his side's concentration, with Fulham's first goal coming from a Micah Richards foul throw, while he also believed that Edin Dzeko was fouled in the build-up to Fulham's equaliser.
"For 10 or 15 minutes after Fulham scored, they played very well," Mancini added. "But a football match is 95 minutes and a top team like us needs to have more control of the game.
"I'm not angry. I'm just disappointed because we conceded two stupid goals."
The Italian also defended his decision to withdraw David Silva, who was replaced by Pablo Zabaleta before Murphy struck.
"In the middle I didn't have any players because we have James Milner and Nigel de Jong out injured," he said. "So I didn't have a chance to change it in the middle."
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