Both world champions said their cars lacked the power to match the speed of the Mercedes that carried George Russell to a dominant pole position ahead of Ferrari's Charles Leclerc.
"The whole qualifying session, I was lacking top speed," said four-time world champion Verstappen, who had been top of the times in his Red Bull in the earlier final free practice session. "The engine was just not working."
"That was one problem and then in Q3, I was about to start my middle lap, but the battery didn't charge.
"So you start a lap with half a battery - so you have to abort and then you lose temperature because you don't have enough power, basically.
"It then snowballs into the final lap and again no top speed and a yellow flag in my lap. That's where you are!
"So, I have no idea for tomorrow. We were in a really good place all week, but then had a disaster of a qualifying because of a lot of issues. Let's see what we can do."
Reigning champion Norris said he felt that a front row grid position was possible in his McLaren, but did not have the power to beat Russell.
"I think P2 was possible," he said. "I felt confident in the car, to be honest, but I just pushed the braking a bit too much."
"I'd rather die trying to get a pole than settle for third, fourth or fifth.
"I'd rather put together a perfect lap than an average lap and I paid the price for that.
"The car's not bad, we're just a long way off -- especially my car is a long way off in the straights. It's limiting because there's lots of straights here.
"Of course, I hope for a podium, but with my straight-line speed it will be impossible."
Verstappen's Red Bull team-mate Isack Hadjar, back in action after missing three races with a broken wrist, qualified an impressive fourth ahead of the Dutchman while Oscar Piastri was third in the second McLaren.
Lewis Hamilton qualified eighth, six places behind Ferrari team-mate Charles Leclerc who he assisted with a 'tow' on his final best lap.
He said: "It was pretty bad in qualifying once again. And it's not for the lack of trying.
"We changed our plan – instead of doing two runs, we ended up waiting and because I was ahead of Charles, I had nobody ahead of me for the tow.
"We just couldn't compete with Mercedes -- they're just outright so much quicker on the straights. They did a great job."