A hectic session was cut short after AlphaTauri’s Yuki Tsunoda and Ferrari’s Carlos Sainz crashed out in the final minutes to bring out the red flag for the fourth time.
Lance Stroll, Antonio Giovinazzi and Daniel Ricciardo had all also found the barriers earlier on.
And Verstappen was clearly seething that his rhythm was constantly being interrupted by crashes, having to settle for P3 with Mercedes’ Hamilton ahead of him and Leclerc on pole in the Ferrari.
The Red Bull driver leads Hamilton by four points in the Drivers’ Championship standings after winning the Monaco Grand Prix last time out and will bid to get past the Briton to preserve that advantage.
But speaking post-qualifying, a disgruntled Verstappen said: “It was a stupid qualifying to be honest. But anyway it is what it is. Still P3. We have a good car. Everything was working out fine.
“But yeah, all this s**t is all the time happening in Q3, I don’t care. It’s just unfortunate. It’s a street circuit so these things can happen. Our car’s strong so I just hope tomorrow in the race we can look after our tyres and score good points.
“We’re still up there. Of course I would’ve liked to start a bit further ahead but it’s still all to play for. Qualifying, a lot of things are happening.
“Maybe in the race these things can happen again. Let’s hope for a clean start and we’ll see from there.
“Yeah of course [it will be fun to battle Lewis]. Three different cars [at the front] as well. It’s always good to have that.”
Red Bull team principal Christian Horner meanwhile told Sky Sports F1: “Max’s frustration, I think he knew after getting purple in sector one and sector two that there was a better lap in there.
“It looked like he picked up a tow from [Fernando] Alonso at the end of the lap too but we’ll never know now. It would’ve been very, very tight. Max was already up on the lap after only three corners and was in a good track position. It’s ifs, buts and maybes.
“We’re P3. Charles did a good job, he’s got the pole. We’re alongside Lewis the championship contender. We’re in good shape.
“I think the good thing compared to Monaco where there’s absolutely no hope of overtaking, here you can overtake, we’ve seen that. It’s about managing the tyres and the grip level.
“We’re going to have to react to that challenge tomorrow. It looks like Mercedes have changed their set-up quite a lot, how that’s going to work out on the longer runs is a bit of an unknown. We’ve got to get our heads down, try get a good start and get stuck into the race.
“Strategy is going to be important. It’s difficult to believe we’ll get through the race without a Safety Car, the amount of red flags we’ve had this afternoon. I think it’s even windier tomorrow so picking our way through the Safety Cars is going to be crucial.”
Pole-sitter Leclerc meanwhile declared: “It was quite a s**t lap I thought! There were two or three corners where I did mistakes but of course I had a big tow from Lewis in the last sector which helped me a little bit.
“Overall I think we would have been there or thereabouts for pole without the slipstream. It’s a good day. I didn’t expect to be as competitive as we were today.
Mercedes have struggled in Baku but Hamilton, who sandwiches Leclerc and Verstappen, is hopeful of an improved Sunday. The reigning world champion said: “We definitely weren’t expecting that. This is such a monumental result for us.
“We’ve been struggling like you wouldn’t believe all weekend. You can see it. We’ve moved around and made so many changes over these two days chasing our tail.
“It’s been so difficult. The work overnight and particularly between the sessions was amazing from the team. I’m really proud of everyone for keeping positive. To be up there and so close to these guys, it’s a great, great start.
“It’s been the biggest challenge we’ve had in a long time, trying to understand what the car really wants. She’s not been happy all weekend. It’s been a bit of a disaster.
“[But] Our race pace is a lot better than our single lap pace. We’re miles off in single laps and a lot closer in race pace. We don’t understand why. I’d like to think hopefully we’re in that same position so we can take the fight to these guys tomorrow.”