Pellegrini's first season at Manchester City ended with a Premier League championship to go along with the Capital One Cup the club had won earlier in the season. If all's well that ends well, then Pellegrini must have been satisfied with how his Manchester City debut turned out.
But Pellegrini surely knows how fortunate last season's title really was, and how his putative No. 1 goalkeeper contrived to make Manchester City's championship run much closer and more difficult than it needed to be.
Hart cost Manchester City at least three points in the first few months of the 2013-14 Premier League season. His misplays and lapses in judgment directly led to dropped points at Cardiff City, Aston Villa and Chelsea.
The blunder at Stamford Bridge was a real killer. It was perhaps Hart's worst mistake of the season, and it deprived Manchester City of a nearly earned point while essentially gifting rival Chelsea two. For a brief time, Hart lost his starting role to Costel Pantilimon.
That Pellegrini could ever have made such a move tells you all you need to know about how poorly Hart was playing at the time.
Those three league points Hart coughed up early were dearly missed as the season wound down. But for Steven Gerrard's epic collapse (physical and otherwise) against Chelsea, Manchester City might never have caught Liverpool to win the Premier League.
Knowing all of this, Pellegrini made an upgrade of his second-choice goalkeeper a priority in the summer transfer window. Pantilimon performed well while Hart was benched, but the towering Romanian goalkeeper was not the sort of player who could lead Manchester City through a Champions League run.
Willy Caballero is, though.
"Caballero joined Malaga, where he teamed up with Pellegrini, in 2011 and went a club-record 480 minutes without conceding a goal," noted BBC Sport on Caballero's signing at Manchester City.
"The most beautiful moments of my career were under Manuel Pellegrini at Malaga, where we achieved big things and we made Malaga's name known around Europe," Caballero told BBC Sport in the same report.
So Pellegrini did not just find a random backup goalkeeper. Pellegrini brought in one of his guys.
With Caballero looming, Hart badly needed to establish himself as a competent, confident and stout No. 1 goalkeeper to prevent his recent shaky history from coming back to mind.
Three matches into the Premier League season, though, Hart has already given Pellegrini cause for pause.
Hart gave up the only goal of the match against Stoke City through his legs. That the strike came from a Mame Diouf semi-breakaway only sort of serves as an excuse for the Manchester City goalkeeper.
"For someone who keeps goal for England, Hart does not inspire confidence in situations such as these. Diouf beat him easily, sliding his shot through the keeper’s legs," wrote Tim Rich for The Independent.
Diouf's goal was a microcosm of the match itself. There was a ton of blame to go around the entire Manchester City side for both the goal and ultimately the loss.
The Diouf strike came from almost nothing after Manchester City cheaply lost possession following a corner kick in the Stoke City end. Then Diouf beat both Aleksandar Kolarov and Fernandinho in the open field to go in on a soft angle against Hart.
Does Joe Hart need to worry about his job after the goal he allowed to Stoke?
Whether or not Hart should have saved Diouf's shot, Manchester City were never going to win a match where they did not score. That the Potters blanked the Sky Blues at the Etihad is inexplicable and for that, every field player in the home colors has something to answer for.
But whenever a team loses 1-0, the sharpest focus is always on the goal conceded. And Hart should have done better.
Manchester City are still even with last season's pace with two wins from three matches. Losing to Stoke City at home, while unacceptable, was not nearly the disgrace that losing at Cardiff City was last season.
Forgive Pellegrini, though, if his trigger finger on Hart is quicker and itchier than it was last season at this time.
Having managed past numerous Hart bungles last season, Pellegrini might reach into his past for a steadier option in Caballero sooner than later.