City opened their Premier League campaign with a 4-0 thumping of Swansea at the Etihad Stadium on Monday night.
It is the kind of dynamic performance the Italian wants to see more of.
"For me, if we win 38 games 1-0, it is okay, but this is impossible," Mancini said.
"It is clear that now we have more offensive players and it is important they all play and maybe that we take more risks than last year.
"This year, we need to score more goals if we want to win the Premier League."
Mancini has splashed out a club record ?38million on Argentina striker Sergio Aguero - scorer of two goals on his debut against Swansea - this summer, and a deal to sign France midfielder Samir Nasri from Arsenal is thought to be nearing conclusion.
The manager is assembling a formidable-looking attack, although he remains keen to stress the importance of forwards tracking back.
"In the Premier League, you need the striker to work for the team because otherwise, it is difficult," Mancini said.
"Wayne Rooney for Manchester United - he scores the goals, but he also works for the team. Didier Drogba is the same for Chelsea.
"This is important - that the mentality is good and that the striker attacks, and then after, he helps his team-mates."
City travel to Bolton, who also got their league season under way with a 4-0 victory, on Sunday.
Owen Coyle's Wanderers team swept QPR aside at Loftus Road last Saturday and Mancini is anticipating a tough encounter.
"Bolton play football very well - for me, they are a strong team," Mancini said.
"They have started the season very well and the game on Sunday will be very hard.
"They were strong last year and had a fantastic season, and they have a good manager. If we want to win we will have to fight for every ball."
City striker Carlos Tevez could be set to make his first appearance of the season in Sunday's game.
Although the 27-year-old handed in a transfer request this summer, a move is yet to materialise and after returning to training with the Blues last week, he will be considered for the match at the Reebok Stadium.
Mancini must also decide whether or not to hand a first start to Aguero following his sensational cameo as a substitute on Monday, while midfielder Nigel de Jong will be assessed after picking up a foot injury.
Source: Team Talk
Source: Team Talk