Defensive midfielder Javi Garcia played the full 90 minutes of Sunday's 1-1 draw with Arsenal while winger Scott Sinclair also made the starting line-up, although he was replaced at half-time by another summer signing, Jack Rodwell.
All three players were signed in August, while Garcia, Sinclair and defender Maicon did not arrive at the club until the final day of the transfer window. Mancini admitted: "We had new players only in the last two or three days of the market, and maybe these players don't know their team-mates well and need time."
City dropped only two points at home all season last campaign, drawing with Sunderland in March, and Mancini knows they need to get back to winning ways as soon as possible. The defending champions are already four points behind Chelsea after three draws from their opening five games.
Mancini added: "The second year after winning a championship is always difficult and I hope we start to win in our next league game, because we need a win. But we need to improve if we are to do that."
City are back in action on Tuesday in the third round of the Capital One Cup against Aston Villa, where Mancini is likely to change his whole team, before a trip to London on Saturday to face in-form Fulham.
Joleon Lescott, who scored City's opener against the Gunners before an 82nd-minute equaliser from Laurent Koscielny, said: "We probably didn't get going as much as we'd like but we showed another side of our game is resilience and unfortunately for us we conceded late on.
"We didn't get in a rhythm for long enough. Arsenal made it hard for us at times and they're a good team, so it's not a negative result but we're used to winning at home and we're bitterly disappointed to concede."
Mancini will include youngsters Denis Suarez, Abdul Razak and Luca Scapuzzi in the squad for Tuesday's game while Carlos Tevez and Mario Balotelli are likely to lead the line after only being used as substitutes against Arsenal.
However, City will be without four players after James Milner and Maicon joined Samir Nasri and Micah Richards on the sidelines. Maicon took a kick to his leg against Madrid and is unlikely to be out for long but Milner is seeing a specialist about a toe problem.
Source: PA
Source: PA