That is the opinion of former City favourite Glyn Pardoe, who also feels the Chilean does not show enough passion.
Pellegrini's position has come under increasing scrutiny in 2015 as his side's Barclays Premier League title defence has faltered.
A shock loss at relegation battlers Burnley on Saturday has all but ended hopes of retaining the crown and it seems only a monumental Champions League victory at the Nou Camp can salvage the campaign.
"It is a win-or-bust game," said Pardoe of Wednesday's last-16 second-leg encounter, in which City must overturn a 2-1 deficit
"It will define our season now after Saturday's result.
"I can't see us winning the league, we are too far behind, but this is a really big one, and not just for the club - for the manager
The pressure would be really on if we get knocked out."
Pellegrini enjoyed a hugely successful first season at the Etihad Stadium.
He restored harmony after the fiery final year of Roberto Mancini's reign and introduced a free-flowing attacking style that delivered the Premier League title and Capital One Cup last year.
But since pulling level with Chelsea at the top on New Year's Day, City have fallen away badly during the second half of this season.
They now trail the Londoners by six points having played a game more and Pardoe wonders if Pellegrini's passive character, which initially served the club so well, could be a hindrance.
The 68-year-old, who made more than 300 league starts for City and helped them to title success in 1968, told Press Association Sport: "It is difficult to say how much pressure he is under.
"I've seen in the paper that he says he is not, but we don't seem to be making any progress and there will come a time where they will think, 'If we're not making progress, let's try somebody else'.
"I honestly don't know how much, but he has got to be under pressure.
"It has been a mixed season
Some things he has done well but sometimes I think he lacks a bit of passion.
"It is good that he doesn't condemn others or complain about things like penalties - I think it's great not to blame anybody else - but he lacks a bit of passion somewhere along the line and I think that gets through to the team sometimes.
"Football is a passionate game and if you haven't got passion you can't play."
Pardoe thinks that part of Pellegrini's problem is that he is not tactically diverse enough, sticking too often to his preferred attacking style and 4-4-2 formation.
He said: "It is difficult when you win things because everybody expects you to do it again the next year, but everyone is ready for you
Teams work you out eventually.
"We haven't got a Plan B
We need to change it sometimes
The way teams defend against us now, you can't always pass through them."
Despite that, and how deflated the team looked at Turf Moor, Pardoe cannot rule out the possibility of a squad still containing several top-class players producing something extraordinary in Barcelona.
He said: "If you can't pick yourself up for playing Barcelona there is something the matter with you.
"If we play with the right attitude we have got a great chance, because they are no great shakes at the back
They are an attacking team
"They get on top and dominate you but if we can get at them, there is no reason why we cannot score two or three goals."
Source : PA
Source: PA