The Chilean is concentrating on developing an attractive style that will win matches, and ultimately silverware, at the Etihad Stadium.
He made a convincing start on Monday as City swept aside Newcastle 4-0 in their opening Barclays Premier League match.
City overran the Magpies with slick attacking play - in keeping with the club's stated desire to play better football than in recent years - but Pellegrini does not expect that to necessarily intimidate opponents.
Pellegrini said: "I don't think they are going to fear us.
"It is very important for us to play the way we played.
"What happens with the other teams, if they fear us or not, I don't think from one match we can have an important conclusion.
"The important thing is that we start winning in our stadium.
"The second important thing is we win the way I want this team to play. What happens in the future we will see."
While there are no concerns over City's attack after Monday's performance, there are worries in defence due to injury.
Influential captain Vincent Kompany limped off after 71 minutes against Newcastle with a groin injury and is expected to be out for at least a month.
Fellow central defender Matija Nastasic only returned to training this week after an ankle injury and is doubtful for Sunday's trip to promoted Cardiff.
With Kolo Toure having left for Liverpool in the summer, Pellegrini's options are otherwise limited.
Midfielder Javi Garcia played out the closing minutes against Newcastle alongside Joleon Lescott in a makeshift back line.
With Micah Richards also troubled by a hamstring injury, the only other fit centre-back is youngster Dedryck Boyata, whose City career has stalled in the past two years with loans to Bolton and FC Twente.
If out for a month, Kompany would also miss next week's clash against Hull and the trip to Stoke after the next international break.
He could come back into contention for the derby against Manchester United on September 22.
News of his condition will also be a concern to Belgium, who play an important World Cup qualifier in Scotland next month.
Pellegrini said: "I would prefer the doctor to say the last word, how many weeks, but he is injured I think for at least one month. The doctor can give more information.
"Today or tomorrow we will know exactly what happens with him."
Nastasic was injured in the Barclays Asia Trophy in Hong Kong in July and it was feared he could miss the first month of the season.
But the Serbian has made a quicker than expected recovery and will ease Pellegrini's worries should he prove his fitness.
Pellegrini said: "Nastasic is working normally with the squad and we will see if he starts or not."
The situation with Kompany will heighten speculation Pellegrini may look to sign a new defender before the upcoming transfer deadline.
City have been linked with Real Madrid's Pepe and Atletico Madrid's Martin Demichelis, formerly of Pellegrini's old club Malaga, but Pellegrini would give no definitive clues.
Speaking at a press conference to preview the game at Cardiff, the Chilean said: "It is not dependent on what happens with Vincent Kompany.
"I told you last week that until the last day we will see what we can do, if we can improve our squad or not.
"But we have a very good squad so we will see what happens in the next days until September 2."
The injuries have given Lescott a chance to re-establish himself after falling down the pecking order under Roberto Mancini last season.
The England international is now in the final year of his contract at the Etihad Stadium and his long-term future is unclear.
Pellegrini did not want to disclose information about whether new discussions had been opened.
He said: "We are not talking about those things this week."
Despite the emphatic nature of Monday's win, which has seen City installed as outright title favourites ahead of Chelsea by many bookmakers, Pellegrini is taking nothing for granted against unfancied Cardiff.
He said: "It will be very difficult.
"We know Cardiff are new in the Premier League this year but I think they are a very good team.
"It is the first game they will play at home they will be a very difficult team."