After Monday's capitulation by Liverpool at Crystal Palace, City can put one hand on the trophy with victory over Aston Villa at the Etihad on Wednesday evening - a game you can see live on Sky Sports 1 from 7pm.
A win would lift them two points clear and, with a vastly superior goal difference, Pellegrini is confident his side will finish the job at home to West Ham on Sunday.
"We have experienced players, they've been in a similar situation two years ago," he said. "We have the pressure to win, but we've had it the whole year.
"From the beginning of the season, I always said that this team wants to win
the title. Now we will try to do it."
Despite his confidence in the team's ability, the Chilean is refusing to discuss the title, insisting the clash with Villa is the only thing on his mind.
"I did not watch Liverpool on Monday as I was watching videos of our opponents tonight," he said.
"The only way to continue in our position is to win the three points and after that we can analyse all the other things when the race is over.
"If I try to be calm, it's because I think it's the best way for the players to play these two games, but I don't want to talk about the title race now."
Striker Sergio Aguero will miss the Villa clash with injury and is also a doubt for City's final match of the season against West Ham.
Pellegrini said: "Sergio couldn't recover 100 per cent from his groin problem, so he is not in the squad list.
"Maybe he can have some chances (for the West Ham match), we will see the way he improves during the week.
"It was not 100 per cent sure if he was completely fit for Wednesday, that is why I didn't want to have a risk with him, but we will see during the week if he can play on Sunday."
City go into the game as odds on favourites for the title with Sky Bet but Gary Neville says they can't be complacent against an Aston Villa side capable of "daft" results.
And Sky Sports expert Neville says Pellegrini must make sure his players are focused on Wednesday night against a side that have also beaten Chelsea and Arsenal this season, but only confirmed their Premier League survival at the weekend.
"They will have to be careful. If you were Pellegrini and the experienced players in the spine of the team who have won a championship before then you would be guarding massively against complacency. They must really prepare to have to win these last two matches.
"Aston Villa put in some daft performances, some performances that surprise you every so often. They are capable of it.
"Aston Villa will be relieved. Those young players have been under pressure in these last few weeks. They could have gone into the weekend, lost the home game and if other results had gone against them they were under huge pressure.
"They'll have probably had a little bit of a celebration, I would think, on Saturday / Sunday which could help them in relieving pressure on Wednesday night. For Manchester City it's purely about them getting their minds right in the next two or three days and not thinking that the job's done.
"It's all transferred towards City. It's City's to lose now."