Handed his first start since his £8million move from Aston Villa, the England international went down with a suspected hamstring injury early in the game and left the field on a stretcher.
Real then took control of the contest at the Melbourne Cricket Ground as Karim Benzema, Cristiano Ronaldo and Pepe scored to make it 3-0.
Yaya Toure replied with a penalty on the stroke of half-time after Sergio Ramos handled from Raheem Sterling’s flick-on.
Both sides made a number of changes in the second half and Real secured victory when substitute Denis Cheryshev tapped in Isco’s cross.
The win means Real secure the International Champions Cup ahead of City, who now start their journey home ahead of the new Premier League season on August 8.
Delph’s participation in City’s opening game of the 2015/16 campaign against West Brom looks in doubt after his debut lasted less than 20 minutes in front of more than 99,000 fans at the MCG.
It was the MCG’s biggest ever crowd for a football-only event and they were treated to plenty of goals in the first half.
The first arrived in the 21st minute when Bale set up Benzema from the right wing, the French striker firing past Joe Hart with a volley from the middle of the box.
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 it clear in vain.
The Spanish giants moved 3-0 up just before the break when Pepe was left unmarked from a corner to head home.
Toure pulled one back for City in first-half stoppage time from the penalty spot after Ramos handled, although the incident appeared to be just outside the box.
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 Cheryshev, who bundled in the ball as it fell at his feet from close range following a surge into the box by Isco, with City unable to gain further traction.