Perez, overall runner-up last year to teammate Max Verstappen, has taken only 15 points from his last six races and has fallen to sixth in the championship at the halfway point of the season.
"Of course, he's under pressure. That's normal in Formula 1 and when you're under-delivering that pressure only mounts," team boss Christian Horner said after Perez started from the pitlane in Sunday's British Grand Prix and finished 17th.
Triple world champion Verstappen, winner of seven races this year and now 84 points clear of McLaren's Lando Norris, was second.
Perez's blank meant resurgent McLaren outscored Red Bull for the fifth time in six races, a rate that could bring that team into the title reckoning.
McLaren boss Zak Brown said last Saturday that Perez's continued under-performance could be a key factor in the championship.
Horner said nothing had gone the Mexican's way at Silverstone, starting with his spin into the gravel in qualifying that had the team boss shaking his head on the pit wall.
"We took a gamble in the race, he started on the hard tyre and was making decent progress early on in the race, the rain started to arrive he was P15 or 16 at the time, you roll the dice a little at that point," Horner said.
"He went on to the inter, if the rain had picked up he'd have looked a hero. It didn't, so you don't.
"Then he had an extra stop and the time loss of being on an inter on a drying track was haemorrhaging a lot of time for him. So yeah, obviously a lot to look at from over the weekend.
"He knows it's unsustainable to not be scoring points," added the Briton.
"We have to be scoring points with that car and he knows that. He knows his role and his target. Nobody is more eager than Checo to get back and find his form again."
Red Bull extended Perez's contract in June, a move that now looks premature although performance clauses could also be triggered.
"Of course, there's frustration when both of your cars aren't performing collectively," said Horner.
"To lose that car in Q1 (first qualifying) was very frustrating.
"Some drivers need an arm around the shoulder and some need a kick up the arse and sometimes it varies from week to week," he added ominously.
