The champions were beaten 2-1 at Crystal Palace on Monday Night Football, rocked by goals from Glenn Murray and Jason Puncheon either side of half-time despite dominating at Selhurst Park.
The result marked City’s third successive away league defeat and their seventh defeat in all competitions since drawing level at the top of table on New Year’s Day, and it leaves them nine points adrift of leaders Chelsea with seven games remaining.
But Pellegrini said: “I’m not concerned about my job. That is one thing I am never concerned with.
“I never have fear about it, I do my work, I’m very happy. The team maybe have a difficult season but never worry about me.
“We are not thinking about Chelsea, or about the title. We are just trying to win our games.”
Pellegrini has refused to concede the title despite the defeat.
He said: “We’re not talking about the title, we just want to win our games. It’s a blow – every time you drop points it’s a big blow. At the end of the season, every point that you lose is costly.
“The next seven games are very important. Normally the champions’ place is just one or two points (above the next team), so we must continue to win as many points as we can. There are 21 to play for.
“We are only thinking about what we can do and that is to try and win our games and at the end of the season we will see where we are in the table.”
City dominated possession and went close through Sergio Aguero, David Silva and Yaya Toure before the latter pulled a goal back with 12 minutes of normal time remaining.
“I am very pleased with the way my team played because I think we played really well,” Pellegrini said.
“Normally we’ll win if we play like this. We had a lot of chances and were unlucky not to score more goals.”