Mancini's side led 2-0 at half-time on Sunday after Joleon Lescott headed in a David Silva free-kick and Edin Dzeko beat United goalkeeper David De Gea from long range.
But the FA Cup winners were unable to hold onto their advantage as United hit back to equalise through Chris Smalling and Nani before the Portugal winger punished a mistake from Vincent Kompany to score the winner in second half stoppage time.
It was a painful way to lose, especially against a bitter rival like United, but Mancini conceded that Sir Alex Ferguson's side had the better of the game so he couldn't complain too much about the result.
The City boss was more concerned that his players understand the reason why they lost -- principly their failure to retain possession well enough to frustrate United -- and make sure they avoid a repeat in the more important matches to come.
"For us it is important we understand why we lost this game. A top team that doesn't play well but scores two goals needs to have a strong mentality," Mancini said.
"If we play a team like United or Real Madrid in the Champions League we need to understand that we must keeping playing football and not sit deep like we did in the second half. We have to learn from this.
"But this is only one game. It was normal to have a tough game because we were not ready 100 percent.
"The positive was the last 20 minutes in the first half. Now this game is finished and next week we start the season."
Mancini's men are under pressure to mount a serious challenge for the Premier League title this season after another close-season of lavish spending.
Losing a two-goal lead against the champions was hardly the most convincing start, but the Italian is sure City will be in the title shake-up come the end of the season.
"I don't think this result will affect us. It is not important for the Premier League, for the FA Cup or anything else," he said."
"United is a top squad in the Premier League. They are better than the other teams but we can challenge at the end of the season for the title."
Not for the first time, Mancini found himself having to defend the antics of City striker Mario Balotelli, who responded to being substituted after a lacklustre display by disappearing straight down the tunnel.
He eventually reappeared on the bench and Mancini preferred to urge Balotelli to improve his game rather than berate him for another show of petulance.
"I didn't see anything. I was concentrating on the game. Now every time Mario does something it seems we talk about it. He can do his job better and play better than today," he said.
Balotelli's place is likely to come under threat from Sergio Aguero once City's ?£38 million record signing is fully fit.
Aguero was an unused substitute at Wembley as he recovers from blisters and his efforts for Argentina at the Copa America and Mancini admitted he might not be ready to start for a few weeks.
"Aguero is not ready to play. Maybe I could put him on for the last 10 minutes," he said. "He needs to train and to recover from the Copa America. He only finished playing three weeks ago."
Source: AFP
Source: AFP