The Chilean's position at the Etihad Stadium has come under scrutiny after last weekend's 2-1 defeat at Liverpool left the champions five points adrift of Premier League leaders Chelsea, who also have a game in hand.
Media speculation has suggested that City - who appointed Pellegrini ahead of the 2013-14 campaign - could attempt to persuade Pep Guardiola to leave German champions Bayern Munich to take the reins.
But Pellegrini is unconcerned by the reports and insists the only time he feels under pressure is when his team fail to perform to their best standard.
"I never have any pressure about the amount of titles," he said. "The only pressure for me is when I see my team not playing in the way I want them to play.
"I repeat, when I signed my contract I was not told I had to win one title every year or five in five years.
"The title is important but not the only important thing."
Pellegrini confirmed he had no fresh injury worries ahead of Wednesday's match with rock-bottom Leicester City, but did hint at changes to his starting XI.
He added: "The whole team is fit, we'll see how players from Sunday recover."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
