Delph, who signed from Aston Villa after making a U-turn over his switch to City last week, lasted less than 20 minutes after a tussle with Luka Modric resulted in his early exit from the International Champions Cup game in Melbourne
City will now face an anxious wait to determine the severity of the injury to their £8million signing, with their opening Barclays Premier League match against West Brom just over two weeks away.
"Unfortunately, it looks like Fabian has a problem with his hamstring - we thought it would be useful for him to play 45 minutes but he got the injury so it's not the best news," Pellegrini told the club's official website.
"We will have a more clear diagnostic from the doctor tomorrow."
The City boss was not too concerned following the heavy defeat by Real at the MCG after fielding an under-strength side.
Eliaquim Mangala did not feature after falling ill ahead of kick-off while Martin Demichelis, Sergio Aguero, Fernandinho, Pablo Zabaleta, Wilfried Bony and Vincent Kompany were also absent from the side.
It meant Jason Denayer partnered 16-year old Cameron Humphreys in defence against a formidable frontline of Cristiano Ronaldo, Isco, Gareth Bale and Karim Benzema
"We knew before the game that it was difficult to play against a team with such good attackers without Mangala, Kompany and Demichelis," Pellegrini said.
"You must also add the other players who are not here: Bony, Aguero, Fernandinho and Zabaleta.
"Especially defending, we knew it would be a difficult game
Mangala was sick this morning so he could not play and Kompany is becoming a father again so is not here.
"I'm not concerned as we had a lot of missing players and then a lot of players have also arrived late so they've worked just five days.
"For them, they're just starting work - it's important in pre-season to work hard and it's good to play against important teams but you can't be worried about winning or losing at this point."
Benzema volleyed the opening goal for Real past City goalkeeper Joe Hart with Ronaldo adding the second shortly after
Pepe made it three with a header from Isco's corner before Yaya Toure pulled one back for City in first-half stoppage time.
However, Real winger Denis Cheryshev added Real's fourth with 15 minutes to go and Manuel Pellegrini's side never looked like launching a comeback.
Hart is also not reading too much into the disjointed performance against Real, telling Sky Sports 1: "It's pre-season at the end of the day
We can't get too wrapped up in the result
"A lot of us haven't had many minutes and we're still missing the South American guys so we're still going to get stronger and fitter for the start of the season."
But the City goalkeeper was impressed with the performance of £49million signing Raheem Sterling, adding: " He got a bit of treatment but that's what he's going to get
You fully expect him to bounce off players but he gets up and keeps going and he's going to be a great player."
Source : PA
Source: PA