Claudio Ranieri's men have pulled five points clear at the top with nine league games remaining, leaving them on track for the unlikeliest of triumphs.
Pellegrini, whose City side are fourth and 10 points off top spot after a 4-0 thrashing of Aston Villa on Saturday, knows his team will need some favours late in the campaign.
And the Chilean said there was no doubt Leicester would be feeling the pressure more than others.
"For every team, whether they have experience of a title run-in or not, there is a lot of pressure in the last part of the season," Pellegrini said.
"Maybe if you are not used to being involved then the pressure is a little bit more, but normally the last five games are very difficult for all the teams because it doesn't matter if you play good or bad you just have to win the games - so nerves are important."
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City's win over Villa saw them end a three-match losing run in the league, but they have games against Manchester United, Chelsea and Arsenal to come late on in the season.
Pellegrini insists his team's focus just needs to be on themselves.
"I think it’s important not to think about how many games we need to win. It’s just important to try to win the next game," he said.
"From now until the end of the season, we must be focused on each game and try to win them.
"We need not only to win our games, but hope Leicester and Tottenham can lose some points."