Pellegrini's comments come after City's title hopes were dented following their embarrassing 2-1 loss to Crystal Palace on Monday.
The defeat leaves City in fourth place on the standings, nine points behind Premier League leaders Chelsea.
"I'm not concerned about my job. That is one thing I am never concerned with," Pellegrini told Sky Sports. "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."
Pellegrini refused to discuss Chelsea or City's chances of retaining the title.
"We are not talking about the title or Chelsea," he said. "We are thinking only about winning our games. That is the only duty we have. Then at the end of the season, we will see which team has the most points with the second place, the third place, the fourth place. We don't think about any more than that.
"Every time you drop points it is a big blow. At the end of the season, every point you drop is costly, but you can lose once playing this way. If we play this way again, normally you win."
Rather surprisingly, Pellegrini was "pleased" with the way his team played despite the loss.
"I am very pleased with the way my team played," he said. "They played really well. From the beginning to the end we had a lot of possession and lots of chances and we lose the game because they score a goal from an offside and a beautiful free kick. That was the only thing they did the whole game.
"We had a lot of chances and we were very unlucky not to score more goals. I don't want to have excuses about referees and the offside goal. It's not the job of the managers to analyse the referees."