The Manchester City boss admits the England goalkeeper had a bad day at the office against Bayern Munich but is confident that he will recover his form by remaining No.1
Hart was beaten at his near post by shots from Franck Ribery and Arjen Robben as Bayern cruised to a 3-1 victory at the Etihad Stadium, leading to speculation that Pellegrini may consider taking him out of the firing line for Saturday's clash with Everton.
However, while acknowledging the need for Hart to pick up his level of performance, the Chilean insisted that he has faith in the 26-year-old's ability.
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"Joe knows he must improve the way he is playing but he knows he has our trust."
City have come in for some criticism for their inconsistent displays this season, having followed up their 4-1 derby mauling of Manchester United by twice surrendering the lead in a 3-2 reverse at Aston Villa on Saturday.
Pellegrini argues that his team deserve more than their haul of 10 points from six games but warned them to expect a tough game with unbeaten Everton, against whom City have lost nine of their last 12 top-flight meetings.
"Everton is the only team unbeaten in the Premier League and they're playing very well but I hope we'll have a good game and get three points," he added.
Martin Demichelis remains sidelined with a knee injury, while Stevan Jovetic is also unavailable due to a "couple of small problems", according to Pellegrini.
The ex-Malaga boss also confirmed that Jack Rodwell has resumed full training after a hamstring problem and is fit but will not feature against his former club.