Verstappen posted a 1min10.727s flying lap to beat Ferrari rival Charles Leclerc to pole position at Interlagos in a shootout that was red-flagged owing to a thunderstorm hitting the track.
While Q3 was almost entirely dry until the stoppage with four minutes to run, Verstappen reckoned changing wind conditions created "terrible" laps as grip levels disappeared.
McLaren racer Oscar Piastri was caught out by the new-found instability as he lost the rear end of his McLaren MCL60 into the final corner. The Australian rookie had been a credible pole contender after setting the best first sector of anyone.
But as he ran over the grass to trigger yellow flags, the closing Perez was forced to back off from his final flying lap, which he reckons would have put him on the front row alongside his team-mate.
Perez said: "We were just incredibly unlucky today. I should have been on the front row.
"My lap was very close to Max's until the last corner, and I found Piastri so I had to back off my lap.
"It meant that I was just position-nowhere. It's very unfortunate because I felt like we had a lot better."
Perez's F1 future is the subject of major speculation as he endures a protracted run of poor form.
He is only 20 points ahead of Mercedes driver Lewis Hamilton in the fight to finish runner-up in the championship and has not finished second to his team-mate in a competitive session since the Italian GP in early September.
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In Brazil, Perez ultimately classified ninth ahead only of McLaren racer Piastri, who did not set a time in Q3 owing to his grassy excursion.
Verstappen's first (18.359s) and second (35.659s) sector times combined for 54.018s. Perez's pair of uninterrupted sectors (18.4611s; 35.835s) added to 54.296s to leave him 0.278s adrift of Verstappen.
That meant he would have theoretically beaten Leclerc (0.294s off) to second place on the grid.
Asked about his prospects of recovering over the rest of the sprint race weekend at Interlagos, Perez said: "I think there are some good points and opportunities to race from here."
