The reigning Premier League champions picked up a 2-1 victory at Craven Cottage thanks to substitute Edin Dzeko's goal three minutes from time.
The Bosnia international's goal followed Sergio Aguero's effort late in the first half, which levelled things up after Mladen Petric's penalty had given the hosts a 10th-minute lead.
Referee Mark Halsey awarded the spot-kick after adjudging Pablo Zabaleta trip on John Arne Riise to be just inside the 18-yard box - a decision that irked Mancini.
"Against Fulham here it is always difficult," the Italian said. "They are a good team, have good players, a good manager.
"This pitch is always a tough for us but the problem is we were 1-0 down and I don't know why because the penalty was not a penalty. We were 1-0 down and Fulham didn't shoot on goal for the first 20 minutes.
"That was a problem but I am happy because the players continued to play well, kept calm and we had a lot of chances."
Asked to clarify why he thought the penalty should not have been awarded, the Italian retorted: "You saw everything. My opinion was that it was out [of the box] and it was no foul, no penalty.
"No, I don't agree it was a penalty. What do you think?"
Mancini claims the incident was the latest in a number of recent decisions that have cost his side.
"We can do nothing," he added. "There were a lot of mistakes in the past four games. We accept this, but we're not happy. This is true but we can do nothing, only continue to play. Sometimes it is a penalty but the referee is there to take a decision. Sometimes he does well, sometimes he can do bad.
"If we go to watch all our last three games, against Stoke it was handball. I don't know why the referee that was behind didn't give it. Against Arsenal there was one penalty."
Yesterday's victory propelled City up the table and stopped the rot after a winless streak that stretched to four matches in all competitions.
While Dzeko will take the headlines for his late goal, Mancini can be just as thankful to Riise for their winner.
The Norwegian left-back failed to clear a Gael Clichy cross, allowing Dzeko to rifle home inside the box and secure three points.
"It was a mistimed ball," Martin Jol, the Fulham manager, said. "I would hit it with my right foot instead of trying to head it. It was a bad clearance.
"I think he will be disappointed because the mistake he made they punished.
"They are a very good team but there is always a possibility against them to play your football like, for example, Arsenal did last week.
"They have to punish them and we couldn't play our style, especially in the second half.
"We couldn't keep the ball, they were stronger than us and more eager to score.
"The only thing we could do was defend, defend, defend and that is probably not enough if you would like a result against them."
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