Verstappen frustrated with 'kangaroo' car in Monaco
The world championship leader complained his car was "jumping like a kangaroo and gave him a headache" and he failed to take pole for the first time this season.
"I'm not disappointed with the position, but with the performance the whole weekend," said the three-time world champion.
"But it's no surprise. I knew our limitations coming into this weekend. We can take kerbs and it's like driving a go-kart with no suspension and no damping."
In a closely-contested session, Ferrari's Monegasque home-town hero Charles Leclerc took pole position ahead of McLaren's Oscar Piastri and Carlos Sainz in the second Ferrari.
"We lose so much speed in the low-speed corners where it is bumpy and the car jumps all around," said the Dutch driver, who had taken pole position in the previous seven races this season.
"I don't think there's much we can do in the race to pass anyone. We just have to stick with them. Anyway, we don't have the fastest car and we are not really out of position."
His Red Bull team-mate Sergio Perez qualified 18th.
"We tried everything this weekend to come up with a successful plan," added Verstappen, "but nothing has worked."
"The car is just so difficult to drive. When you look at Checo (Perez), that says it all. He is normally great on street circuits but today shows we have some pretty dramatic problems."