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 £8 million signing, with their opening Barclays Premier League match against West Bromwich Albion 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 last night.
“We will have a more clear diagnostic from the doctor tomorrow.”
The City manager 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, who spent last season on loan at Celtic, 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.”
After an evenly-matched start, City were dealt a double blow when Delph went down following a challenge with Modric and then Bale then set up Benzema from the right wing, the French striker firing past Joe Hart from the middle of the box in the 21st minute.
Ronaldo quickly doubled Real’s advantage when Toni Kroos launched a perfectly-weighted ball to his feet before the Portuguese wriggled clear of Aleksandar Kolarov to chip into the net. Hart parried the ball but it went backwards and over the line, with his scrambled efforts to scoop clear in vain.
The Spanish giants moved 3-0 up just before the break from the set-piece when Isco sent in a corner and found Pepe, who climbed the highest in the box from ten yards out to power a header past the motionless Hart.
Yaya Toure pulled one back for City in first-half stoppage time from the penalty spot after Sergio Ramos handled the ball following a flick-on by Raheem Sterling.
After the break, Real went close twice in quick succession around the hour mark when Ronaldo almost played in Isco with a one-two before the Portuguese playmaker burst into the box and fancy footwork almost undid the City defence with a shot that crept wide.
Real did add a fourth in the 73rd minute through Denis Cheryshev, who bundled in the ball as it fell at his feet from close range following a surge into the box by Isco, and Pellegrini’s side never looked like launching a comeback.
Meanwhile, Real boss Rafael Benitez is confident Ramos and Benzema will remain at the club amid reports linking the pair with moves to England.
Ramos is reportedly at the centre of a tug of war between the Spanish giants and Manchester United, with rumours suggesting the defender wants a switch to the Barclays Premier League.
Benitez said: “Sergio has known from day one that I want him to stay and I’m sure that he’ll stay with us.”
The former Liverpool, Chelsea and Inter Milan boss was also optimistic of Benzema remaining in the Spanish capital, despite reported interest from Arsenal.
Benitez added: “In this case Karim is our player so I will not talk about that. I hope, I’m sure, that he will stay with us.”