Hart's status as England's first choice has come under renewed scrutiny after an error in the midweek friendly against Scotland at Wembley.
The 26-year-old was widely thought to have slipped below the high standards he set during City's 2011-12 title-winning campaign last season.
England boss Roy Hodgson has backed his keeper but added that form will be important in a season he hopes will end with a trip to the World Cup in Brazil.
Pellegrini said: "I haven't spoken with him - maybe tomorrow [Saturday] we will (speak) - but I think Joe Hart has to demonstrate why he is the best goalkeeper in England every week he plays.
"He is a very important goalkeeper, I have a lot of trust in him.
"Everyone can make an error in one match but personally I have a lot of trust in Joe Hart.
"I don't have any problem with his performance. I am sure he will again this year demonstrate why is the number one in England."
City begin their latest Barclays Premier League campaign when they host Newcastle at the Etihad Stadium on Monday.
Pellegrini's appointment over the summer, coupled with the new signings of Fernandinho, Jesus Navas, Stevan Jovetic and Alvaro Negredo, has changed the mood at the club.
Last season ended on a sour note as City conceded the title to Manchester United and were beaten by underdogs Wigan in the FA Cup final.
Pellegrini is happy with how his squad has settled and is ready for the twin challenges of the Premier League and Champions League.
He said: "I am very pleased. I think we have the squad we need for the year, for important competitions - not only for the Premier League but also the Champions League."
City's summer signings were all completed early in the close-season window but Pellegrini has not ruled out further additions before the transfer deadline on September 2.
It has been suggested City could attempt to sign another defender after Matija Nastasic was injured playing in the Asia Trophy last month.
Pellegrini said: "We will see. We don't need to finish today. Maybe not, but maybe yes also."
Nastasic, however, appears to be making good progress in his recovery from his ankle problem.
There were fears the Serbian could miss the first month of the campaign but he now looks set to resume full training next week after taking part in a light session part open to media on Friday.
Pellegrini said: "I am not surprised because we saw him work hard in the last week.
"He is not ready for the next match but I think next week he will work normally with the whole squad."
Striker Sergio Aguero is in contention to face the Magpies after overcoming the knee injury that has prevented him playing during pre-season.
Pellegrini said: "He is fine, no problem. He has worked with us normally for the last 10 days so he is not a problem."
Pellegrini, speaking at a regular press conference to preview the Newcastle match, also revealed winger Scott Sinclair could be allowed out on loan.
The 24-year-old failed to make a major impact after joining City in a £6.2million move from Swansea last summer, making just three starts.
He missed the end of last season after requiring surgery to remove a blood clot but has made a full recovery and has been linked with a temporary switch to West Brom.
West Ham and Crystal Palace are also reportedly interested in a player who, after coming through the youth ranks at Chelsea, has been out on loan six times during his career.
Pellegrini said: "Scott Sinclair is here and in the squad.
"He wants to play more and in this squad he has important players that play in the same position.
"We will see what happens with him today [Friday] and tomorrow [Saturday] but if he wants to go on loan to play more, we will try to give him that, only if he agrees to it."