Though Sir Alex Ferguson's side emerged victors thanks to Robin van Persie's injury-time free-kick, allowing United to stride six points clear at the Barclays Premier League summit, Mancini felt his team were the better side.
The Italian believes the championship race could turn City's way once United return to Champions League action, although before then he has to cope with an injury list which will be compounded by the absence of Yaya and Kolo Toure at the African Nations Cup next month.
"We showed last week that we are better than Manchester United," said Mancini.
"They do have more experience than us. They don't have any problems when they are behind. They continue to work.
"We should do the same. It only depends on us whether we can recover these points.
"But the season is long and everything might change in February when the Champions League starts again."
Mancini remains resolute in the belief he has in City's squad, even though they have rarely hit the heights which drew so much attention at the start of last season.
"Probably it is true," he said.
"But we are only six points behind and in second position.
"We don't have a big problem. I still believe in these players and we do have a chance."
Yet there are issues for Mancini to address.
For a start he has virtually abandoned hope of persuading the Toure brothers to remain in Manchester rather than report for Ivory Coast duty.
And given past examples, even his hope that the pair will be available for the FA Cup tie with Watford on January 5 may prove optimistic.
Of more immediate concern, Vincent Kompany's hamstring injury looks certain to rule him out of Saturday's trip to Newcastle.
"We will try but it is difficult," said Mancini, adding the Belgian had "probably a two per cent chance" of playing at St James' Park.
Then there are reports of dressing room unrest, specifically rows with both Joe Hart and Mario Balotelli immediately after the United defeat.
In both instances, it is easy to see why Mancini might have a problem.
He called for a four-man wall at the fateful free-kick from which Van Persie scored the winner, only for Hart to overrule him to get Carlos Tevez to mark Wayne Rooney.
If Mancini's public condemnation of Balotelli's inept display was repeated behind closed doors, the fiery Italian is unlikely to have been too impressed.
"It is usual for me to talk to the players," said Mancini.
"Also sometimes you can have a discussion.
"But I prefer to keep it in the dressing room, not like some other people who talk outside.
"For me it is not like this. We know where these stories come from."
It is not the best of backdrops from which to approach a trip to Tyneside.
Newcastle are not even close to the form which saw them secure a fifth-placed finish last term, but Mancini concedes City do not have the same swagger which brought them such a crucial victory on the penultimate weekend of last term.
"Last year was different," said Mancini.
"We were in a strong moment and won the last six games.
"This year is not the same.
"They are a very good team with a very good manager."