City blew the chance to open a top-flight campaign with five straight victories when Fulham came from 2-0 down to draw Sunday's clash at Craven Cottage.
The result was the first blow to the visitors' title hopes and, coming four days after they made their Champions League bow, it cast doubt on their ability to cope with the twin demands of domestic and European football.
And manager Mancini bemoaned his inability to rest the likes of Yaya Toure and Gareth Barry with James Milner and Nigel De Jong currently sidelined through injury.
Asked if that meant he did not have enough players, he added: "We are lacking at this moment because we lost two midfielders.
"I don't have players at the moment. I can only change the full-backs.
"I have only two midfielders, because James and De Jong have injuries."
Mancini also appeared to admit his players lacked the mentality of champions after watching them waste numerous chances to kill off opponents for the third time in eight days.
"What team comes here against Fulham in London and has over 70% of ball possession?" he added.
"We had the same problem against Wigan at home. We had 15 chances in the first half and we scored only one goal.
"It doesn't always go well if you don't score, if you don't close the game."
Mancini was unhappy with the way his star-studded attackers defended, too, accusing them of shirking their responsibilities.
"For 10 minutes, we defended with five or six players. It is not good enough," he said.
"I'm not angry. I'm just disappointed because we conceded two stupid goals."
Those were scored by Bobby Zamora and Danny Murphy after Sergio Aguero continued his sensational start to life in England with the seventh and eighth goals of his five-game Premier League career.
Fulham should have been even more tired than their opponents, having had 24 hours less of a rest after their Europa League game.
But after a lethargic first half, they were full of beans in the second, fighting back to haul themselves off the foot of the table.
Manager Martin Jol, who is still searching for his first league win in charge, admitted being bottom had been "awful".
He added: "We played two away games and had to play in Europe as well so it wasn't easy, but you have to win your home games.
"Luckily enough, for now, we are 18th. It looks better."