It marks a stark change in approach from Mancini, who was criticised last season for being too defensive, as his team have notched 15 goals on their way to four wins out of four in the Premier League this term.
Their scintillating start has been eclipsed by neighbours United, who are top on goal difference having scored 18 including last month's 8-2 drubbing of Arsenal, but City's form may well be motivating the champions according to Mancini.
"When they [United] played against Arsenal, they continued to try to score, also for us we need to have this mentality," the Italian told a news conference.
"If we have a game like in Tottenham when we can score we need to continue to play, play, play, to score always."
City came away from Spurs with a 5-1 win on the same day that United beat Arsenal and had striker Edin Dzeko to thank for four goals.
Last weekend they hammered Wigan Athletic 3-0 at home with all the goals coming from Argentina forward Sergio Aguero in a game where they squandered many other chances.
Sunday's opponents Fulham will not be relishing a more attack-minded City, having lost 4-1 to them in this fixture last year in one of the visitors' most fluent performances of the season.
Critics branded Mancini a bit too 'Italian' for his cautious approach to some games last term where a one-goal lead was often defended rather than built upon.
His team were booed by their own supporters at times last term, while opposing fans joined in too such as at Emirates Stadium after a 0-0 draw with Arsenal.
At the time, Mancini shrugged off the accusations that his team were boring saying: "I prefer boos in the end and to go home with one point rather than with three goals in our net."
Now he seems to want three goals and three points although he is realistic about whether his strikers can continue at their current rate.
"I think today they play very well all the strikers," he said. "But it is impossible to score every game."
They found out they would not get everything their own way when they made their Champions League debut on Wednesday against a Napoli side who defended in numbers and waited for the opportunity for a counter-attack.
City had several chances to score in that game but in the end had to come from behind with an Aleksandar Kolarov free-kick to draw 1-1.
"We need to improve in the Champions League," Mancini said. "I'm sure in our next game in Munich [against Bayern] we will do much better than on Wednesday."
