Second-half goals from summer signing Fashion Sakala and substitute Cedric Itten gave Rangers a major boost ahead of the start of their title defence, which comes next Saturday against Livingston at Ibrox.
Rangers were held to a goalless draw by Brighton on Saturday but Gerrard had been happy with their “dominant” display, and they stepped up a gear against the Spanish giants in front of about 12,500 fans at Ibrox.
Gerrard said on his club’s website: “First and foremost, we deserved the win and we have been excellent over the whole weekend.
“Obviously, it was two different teams for obvious reasons, but every single person over the course of the two 90 minutes has been excellent and they have given me a lot to think about in the two days in terms of picking teams for real next week.
“That is the problem I wanted – to challenge the team, and could they build on yesterday’s performance, and to be fair, they have backed it up.
“It shows the quality and the strength in depth we have got around the dressing room, so I am really happy and content, but at the same time, it is important we stay calm.
“We have two down days now just to recover and get ready, and from Wednesday, it is important that everyone’s focus is top and ready for Livingston.
“We have got valuable minutes into important players and we have shown a level out of possession that I really like – our speed across the grass, our aggression and moving together as a unit in our shape, I am really happy with that and yesterday, we did a lot of things right but we missed a little bit of magic in the final third in terms of our outcomes, but today, we found that magic.
“It was two great finishes from the boys and they will get a lot of plaudits, but for me, I am more pleased with the two performances from everyone over the weekend.”
Rangers brought Filip Helander into the team and started with Sakala up front in the absence of Alfredo Morelos, who was granted extra time off after his Copa America duties with Colombia.
Real were without their Euro 2020 players but their team included the likes of Marcelo, Luka Jovic, Martin Odegaard and Isco.
Sakala missed a couple of chances before the visitors took the lead in the eighth minute when Rodrygo rode a challenge and netted.
Rangers had a series of first-half chances, with Ryan Kent hitting the bar from close range, before Sakala powered home an equaliser in the 55th minute after being set up by Glen Kamara’s pressing.
Nacho was sent off in the 75th minute after picking up a second yellow card for a foul on Kamara and Itten soon swivelled and fired into the corner after Real failed to clear a cross.