Perez went off at the exit of the iconic Parabolica corner, bringing out a second red flag in the session topped by Ferrari's Carlos Sainz.
Perez was fortunate to escape with only minor contact with the outside barriers, tapping the wall with his rear wing.
Explaining the crash Perez said: "I understeered off on the exit and I tried to keep it nailed. I thought I had it under control but then I touched a bit of the gravel and that was game over.
"It doesn't look too bad, the damage. It was fairly small, so I don't think we lost anything in the end. A few laps, so nothing representative in that regard."
The incident didn't dent an otherwise "very strong" session for Perez, calling it his "best Friday in a while" after finding a solid set-up baseline with the RB19.
"The positive is that the car is performing well. I'm feeling comfortable with it," he explained after finishing third-fastest just 0.185s behind pacesetter Sainz.
"And I think we are in a good position for the rest of the weekend. I really felt that we had a very strong Friday.
"This has been the best Friday in a while for us. I think we found some positive steps in the car, so hopefully we can show it all tomorrow and on Sunday."
Team-mate Max Verstappen thought he had more "fine-tuning" to do after finishing 0.276s in arrears, although the Dutchman added that he was hindered on his quickest lap.
"We have been trying a few different wing levels and we still need to analyse what way to go, it's sometimes a tricky thing around Monza," said the double world champion.
"From my side, it probably could have been a little bit better. We're still fine-tuning a bit from low speed to high speed, but I'm quite confident we will get there.
"Also, I was a bit interrupted in FP2 to get a proper read on a few things. But still a bit of work to do.
"On the short run I was blocked a bit in sector two and then in the long run we didn't really get to do a lot of laps, so you don't really get a good idea on it.
"I think on our side we can do a better job, but it's not been the end of the world."
