This is what Manchester City have staked part of their reputation on. That Pellegrini's brand of football can deliver what his predecessor's could not: European success.
It may seem extraordinary, but since Roberto Mancini took City back into the Champions League, the biggest scalp they've taken - not including two Matchday Six wins against an already qualified Bayern Munich - is that of Villarreal … in the season they were relegated from the Spanish top flight.
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While the popular narrative is that Mancini was axed because he somehow self-destructed, rowed with everyone and burned every bridge inside the club, reality is that a few deep runs into Europe and a couple of memorable Champions League nights might have turned things in a different direction.
Ultimately, it's amazing how some success in the Big Cup - when you've already won domestically - can turn stubborness (bad) into single-mindedness (good) or aloofness (bad) into professionalism (good). Particularly when you won an FA Cup and a Premier League title in the previous two seasons.
To read some reports, you would think that Tata Martino's Barcelona are an imploding house of cards: the president forced to resign, Lionel Messi dealing with injuries and tax authorities, Victor Valdes on his way out, Xavi and Andres Iniesta showing signs of wear and tear. And yet, going into the weekend, they were still top of La Liga and on pace to gain 94 points, which is five more than Pep Guardiola's treble-winners of 2008/09. This is a club that take the Champions League semi-finals for granted and rightly so: they've reached Europe's final four in each of the last six seasons.
On paper, it's all set up for a slugfest. Barcelona have kept one clean sheet in the past five outings. That's what happens when you give the ball away more often than you used to - a by-product of Martino's more direct style - and when your back four still includes an under-sized recycled midfielder (Javier Mascherano) and two wingers masquerading as full-backs (Dani Alves and Jordi Alba).
And City have also had their defensive wobbles, particularly in the absence of Fernandinho, who will likely miss this game. Watford scored two (at Eastlands no less), Chelsea one (but it could have been three) and even when they don't concede they often appear vulnerable on the break and on set pieces. With Sergio Aguero also doubtful, the concern is that they won't be quite as free-flowing at the other end of the pitch either.
That's where Pellegrini needs to have a plan. If Aguero is out, the "twin tower" approach of Alvaro Negredo and Edin Dzeko may be tempting against the smallish Barcelona back four. But playing two big men makes sense when you're likely to see plenty of possession and given the absences in midfield, it's not something you can count on. He needs something special, doesn't have long to put it together and he needs to do so in the aftermath of last night's Chelsea game. This is his time to sink or swim.
Liverpool's own boss, Brendan Rodgers, likened his team to Chihuauas. Between this and Jose Mourinho comparing his Chelsea team to a baby horse who "needs its mother's milk" there is no end to the length managers will go to depict themselves as underdogs.
But Rodgers has a point. As stunning as Liverpool can look when they're on the front foot, this is also a team that has had more than their share of defensive wobbles. Martin Skrtel has worked with a rotating cast of characters in either a back four or, occasionally, a back three. Glen Johnson has been the second most present defender on this team and he has started less than two-thirds of the Reds' league games.
Equally, the long-term injury to Lucas means Steven Gerrard is now, effectively, the team's deep-lying holding midfielder. That's fine when they have possession and can spray it about, less so when the opposition breaks, as we saw earlier this year against Aston Villa.
If this team is going to succeed this season - whether it's today at Arsenal in the FA Cup, or, in the league, finishing in the top four - it will need to so the way they have been doing it all season: unconventionally. Stun your opponent with the free-flowing front four and hope the back end holds up.
As of yesterday, Fulham had a first team manager (Felix Magath), a first team coach (Mick Priest), a first team technical director (Alan Curbishley), a head coach (Rene Meulensteen) and an assistant head coach (Ray Wilkins).
Confused? Yeah, so am I.
Magath was appointed on Friday, sharing the news via his Facebook page. It's unclear whether Meulensteen or Curbishley or anyone else knew the former Bundesliga winner had been given the job when Magath made his Facebook post.
Fulham said in a club statement that they would announce a backroom staff reshuffle in due course and that may have more to do with lawyers, employment tribunals and payoffs than anything else. But you do wonder what the purpose was of employing Meulensteen, Wilkins and Curbishley for less than three months before bringing in Magath.
The German boss comes with a reputation as an autocratic disciplinarian, but also an impressive CV. At least, when he's had the resources, he delivered in style, winning back-to-back Doubles at Bayern Munich and delivering Wolfsburg's first Bundesliga title.
(He did less well at Schalke, where money was a bit tighter.)
A quote from midfielder Lewis Holtby, on loan from Spurs, is telling. A while ago he was asked about the prospect of working under Louis Van Gaal: "I wouldn't have a problem with him. I survived under Magath, I can survive anything."
Fulham are hoping that Magath's drill sergeant ways can help them stay in the top-flight, It may work - but even if it does, you wonder about the long-term vision - or lack thereof - at this club.