City remain second in the table, a point behind leaders Arsenal, following a 3-2 win at Swansea on New Year's Day, in what is developing into one of the tightest title battles for many a season.
As it stands, the top six sides are within eight points of the top of the table.
Given City's financial resources and the undoubted depth and quality of their squad, there are many who believe the Citizens should go on and lift the trophy.
Pellegrini is confident his players can handle that pressure.
"I think it's impossible to be in a good team if you don't want pressure, you must be used to playing with pressure," he said.
"I think all the other teams have the same pressure - Chelsea, Arsenal, Liverpool, Manchester United, Tottenham, Everton.
"If they want to say that the pressure is on Manchester City it's no problem for us."
Swansea's situation is rather different, with the Welsh club sitting just four points above the relegation zone with league fixture against Manchester United and Tottenham looming on the horizon.
The Swansea have not won in six league games; their last three-point haul came against Newcastle in the first week of December.
But manager Michael Laudrup believes the performances of his players mean Swansea will soon start to pick up points.
He said: "Seeing that the team is confident is very important to me. To see the players have that confidence in their own skills because that is what we need.
"If you suddenly have three, four or five players lacking confidence that could be a problem. You can start to worry, but I see a team with a lot of confidence so I am sure the points will come as long as we continue to play like this."
Laudrup is likely to bring in a forward during the January transfer window with Michu and Nathan Dyer sidelined by ankle injuries.
The Dane has been linked with moves for Liverpool striker Iago Aspas and Blackpool winger Tom Ince, both of whom were the subject of interest from Swansea in the summer.
But Laudrup was coy when asked about the possibility of Ince making the move to south Wales this month.
He said: "He is a player who has been mentioned before and he is a talented player. But what more can I say? There are a lot of talented players out there and I think a lot of players will be linked with us and other teams in the near future so that is all I can say."