RBR and Verstappen have looked well on course to add respective fourth and fifth constructors' and drivers' world titles this season, and they might have been optimistic ahead of this season's race in the principality.
Verstappen took the win at the corresponding event last season, and had won five of seven grands prix coming into this one.
But he finished nearly 14 seconds off Charles Leclerc's race-setting time, and saw his cushion on the Monegasque at the top of the drivers' standings cut to 31 points.
That was significantly better than Red Bull teammate Perez managed - the Mexican crashed out in the first lap in a collision that also took out Haas pair Nico Hulkenberg and Kevin Magnussen.
Max Verstappen was only sixth in MonacoJos Verstappen has questioned RBR's future
Verstappen: 'Red Bull dominance at an end'
Monaco could be dismissed as statistical noise, but Verstappen's father Jos - himself a former F1 driver - has sounded the alarm.
"They will have to do something about it, understand where certain difficulties come from," he told De Telegraaf. "Meanwhile, it's clear that McLaren and Ferrari are getting closer and closer.
"Max has been good at hiding some of the problems, but you can see how big the difference is between him and his team-mate.
"It seems to me that Red Bull's period of dominance has come to an end."
Speculation around Verstappen junior's Red Bull future persists, with the team enduring a tumultuous time off-track this season.
Team principle Christian Horner maintains his innocence against an ongoing sexual misconduct accusation, while it is against that backdrop that technical genius Adrian Newey's future is so uncertain.
GP BAHRAIN
29 Feb - 2 Mar
GP SAUDI ARABIA
7 - 9 Mar
GP AUSTRALIA
22 - 24 Mar
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5 - 7 Apr
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19 - 21 Apr
GP USA
3 - 5 May
GP ITALY
17 - 19 May
GP MONACO
24 - 26 May
GP CANADA
7 - 9 Jun
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21 - 23 Jun
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28 - 30 Jun
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5 - 7 Jul
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19 - 21 Jul
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26 - 28 Jul
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23 - 25 Aug
GP AZERBAIJAN
13 - 15 Sep
GP SINGAPORE
20 - 22 Sep
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