On his first run in Q2 Verstappen suddenly slowed in the second sector of Jeddah's Corniche street circuit.
The Dutchman notified his team of a possible engine issue, but after he made it back to the Red Bull garage the team confirmed he was hit by a driveshaft problem. As he hadn't set a time yet, that meant the world champion finished Q2 in 15th place.
Verstappen, who won the season-opening race in Bahrain earlier this month, said it was "annoying" to be encountering the issue in qualifying after enjoying a smooth weekend until that point.
"It was the first time I heard about that [issue]. Coming out of Turn 10 it happens, which is very annoying for it to happen," he told Sky.
"I think we so far had a really good weekend, every session was going really well and every time we went on track the car was working really well.
"So now it's a little bit more tricky to get to the front, but it's all about scoring points.
"It's a very long season, of course, I would have hoped to start a bit further up the road, but we cannot change that now."
When asked if he can still challenge for the win from 15th in his rapid Red Bull RB19, Verstappen said it was tough but possible, preferring to stay realistic.
"Anything is possible at this track. We've seen a lot of crazy things, but also we have to stay a little bit realistic," he thought.
"It's going to be tough, but we have good pace, so for sure we'll move forward."
Verstappen's mechanical failure meant his team-mate Sergio Perez become the frontrunner for pole position and the Mexican delivered.
In Q3, Perez edged out Ferrari's Charles Leclerc by less than two tenths, while Fernando Alonso qualified third in the Aston Martin.
