Pressure on Pellegrini has continued to mount this week with the highly-rated Jurgen Klopp, who has announced he will leave Borussia Dortmund at the end of the season, being linked with his job.
This has come after last weekend's emphatic derby loss to Manchester United surely killed any remaining faint hope of retaining the Barclays Premier League title.
Pellegrini said: "Every time you manage an important club, not just here in Manchester City, every big club, if you don't have the results the club deserves, everyone is talking of changing the manager - here, in Spain, in Italy, in other parts of the world.
"So you must be used to the rumours, but I trust a lot in the work I do.
"Of course nobody is happy when you are out of the fight for the title
Maybe you cannot win the title every year but it is very easy (to say) that same thing, to sack the manager
I don't think it is the correct diagnostic for every team."
City are not thought to be considering Pellegrini's future at present, having been satisfied with his performance in his first season in charge.
But the Chilean's position is likely to be discussed when the club hierarchy conduct their usual annual review at the end of the season.
Pellegrini accepts that results between now and the end of the campaign could have a huge bearing on the outcome of any appraisal.
The 61-year-old said: "Every time you finish the season you must analyse, winning or losing.
"I don't think if we lost the next six games it will be the same analysis as if we win the next six games
Maybe winning the six games you finish second, maybe losing the six you finish eighth - so it is impossible to make the same analysis
After that you must review the whole season."
City pulled level with Chelsea at the top of the table on New Year's Day but have badly faltered since, winning just four of 12 league games.
Their recent record is a dismal six defeats in eight games in all competitions and they are now fourth in the Premier League, 12 points behind Chelsea having played a game more.
Their problems might not yet be over either, with Liverpool and Southampton, in fifth and sixth, not yet giving up on Champions League qualification.
Pellegrini said: "I think that for every big team it is very important to be involved in the Champions League.
"We are at this moment - for the first two weeks - out of the top two positions
We have been the second team the whole season, so we are not doing so badly.
"We lost the last two games so it is very important for a big team to be involved every year in the Champions League
Nobody is happy with the performances we have had this year as a squad."
Asked if he needed to finish in the top four to keep his job, Pellegrini said: "I am not thinking about next year
I have a contract for one year more.
"I continue working because I know I have the support of the owners, the players, the fans, everyone - so we need all of them behind the club for these last games.
"I don't feel any pressure about that
I am not thinking about the future."
Pellegrini, speaking at a press conference to preview Sunday's home clash against West Ham, was similarly defensive when asked about the future of Yaya Toure.
Toure has failed to replicate the dynamic midfield performances which proved such a key factor in the title successes of 2012 and 2014 this season.
It has been suggested the 31-year-old, reportedly the club's highest earner, he could be offloaded this summer but Pellegrini insists not.
He said: "We are not talking about that
Yaya is a very important player for our team.
"Maybe all of you are waiting to criticise him or (for us to) sacrifice him but Yaya will continue playing here because he is a very important player for me and the squad and for everyone."
Source : PA
Source: PA