Aguero, the club's record signing at ?38million, made a sensational City debut on Monday night by coming off the bench to score twice and set up another goal.
The Argentina forward's devastating performance, which began only when he was introduced in the 60th minute, propelled City to an emphatic 4-0 win over Swansea in their Premier League opener.
With Silva and Toure also impressing in the Etihad Stadium rout - and the prospect Aguero could also combine with Carlos Tevez and Mario Balotelli if the pair can be brought onside - City would appear genuine title contenders.
Mancini said: "I think Sergio needs to play more with his team-mates to get better.
"We have incredible players like David Silva and Yaya, who speak the same language.
"I think he needs to improve with the team."
Swansea initially acquitted themselves well as they made their top-flight entrance following last season's dramatic play-off promotion.
Yet by the end of the first half the hosts were dominant having hit the bar twice and forced a number of saves from new Swans goalkeeper Michel Vorm.
Edin Dzeko finally broke the deadlock after 57 minutes and Aguero quickly turned a hard-fought victory into a rout.
It was a clear warning to other sides with title ambitions, most notably champions and neighbours Manchester United.
Mancini added: "It was really important to start very well because United won - but it is always important to start the season well."
Aguero is determined to build on his flying start to life as a City player.
Having played in the Copa America last month and started pre-season training late, the 23-year-old playmaker was held back throughout last week's Community Shield and for a further 60 minutes on Monday night.
The former Atletico Madrid forward quickly set about making up for lost time and told City TV: "I am happy. The start was really good and I want to keep like this. It was nice.
"I had a chance to play a little bit and I enjoyed it.
"I helped the team and I want to keep doing the same in the future."
For Swansea, the match was a harsh introduction to the Premier League.
Yet manager Brendan Rodgers could still pick out a number of positives, not least in the performance during a goalless first half and the display of debutant Vorm.
The Dutchman, a ?1.5million signing from Utrecht, pulled off a string of excellent stops including one world-class effort to deny Silva.
The Welsh side will now hope to build on that as they host the Wigan side of their former manager Roberto Martinez on Saturday.
Vorm told Swans Player: "I think it was the busiest match I have ever played in.
"In the first 20-25 minutes we played very well, in the second half you hope you get some chances but they have such good quality players.
"If we had won or drawn it would have been a bonus, we don't need to win these kind of matches, Saturday is much more important.
"These are games we can win and if we play like we did in the first half, we can create chances.
"Wigan have quality, but not the kind of quality City have and it's important to play the same way Saturday and take the three points."
Vorm could do little to prevent defeat once the hosts had gone ahead but Rodgers felt the scoreline was harsh on the keeper.
Rodgers said on Monday: "It's a funny one, you lose 4-0 but many players have shown up tonight, none more so than Michel.
"It is very much a team game but you have got to give big credit to him, he only came into the club on Thursday.
"You can see why he is the Dutch number two but he will improve and adapt. I think he will end up being a very good signing for us."
Source: Team Talk
Source: Team Talk