Verstappen had set two purple sectors in his last flying lap for Red Bull as he sought to seal first on the grid for Sunday’s race.
But the championship-chasing 24-year-old hit the wall on the exit of the final corner which ended his session early and meant he could not improve on P3.
Verstappen broke his rear suspension and is now desperately hoping he has not suffered gearbox damage. Fitting a new gearbox would incur a five-place grid drop.
The incident means Hamilton and Valtteri Bottas in the other Mercedes start ahead of Verstappen, who still goes into the race eight points clear of the former in the Drivers’ Championship.
And Horner admits the Jeddah street circuit will make it difficult for Verstappen to secure a race win that would be huge to his hopes of taking the title, but has told the Silver Arrows his driver will not dwell on his crash.
Speaking to Sky Sports F1 after qualifying, Horner said: “I think it’s going to be very hard to overtake here. It’s going to be strategy, what happens with safety cars, reliability etc.
“We’ll see. Grid position on any street circuit is crucial. We keep fighting.
“If he’d have finished that lap it’d be a very different conversation we’re having. It’s still P3 on the grid, the points are at the end of the Grand Prix.
“We’re going to give it everything we’ve got. Things haven’t gone our way today and that’s motor racing sometimes.
“We’ll keep pushing, we’ll keep fighting. He’ll come back strong tomorrow.”
Hamilton escaped punishment for two final practice incidents, having been summoned to the stewards for an alleged failure to slow during double-waved yellow flags and also for blocking Haas’ Nikita Mazepin.
The seven-time world champion was cleared for the yellow flag incident with it deemed that the yellow light panel had been accidentally activated for less than a second.
But the Briton was reprimanded for his near-miss with Mazepin in FP3, which could have led to a nasty collision.
The stewards also handed a €25,000 to Mercedes over the Turn 8 incident, which occurred when Hamilton was going round slowly and Mazepin was on a fast lap behind him.
Red Bull can protest the decision of the stewards not to hit Hamilton with any punishment for either incident, provided they do so within an allotted time window.
And Horner added: “We’ll have a good look at it. It feels a little inconsistent with what we’ve seen two weeks ago, so we have the right to an appeal.
“We’ll have a look at the information we’ve got. We hadn’t looked at it. These decisions are so late. The team had to focus on qualifying.
“We’ll have a look and see if there’s anything untoward. The one thing we desperately want is just consistency.
“We’ll have a good look. The problem is, if there is an appeal, it’ll be heard here, it’s the same stewards, I’m sure it’ll be the same decision.
“We haven’t seen all the evidence, we haven’t scrutinised it. We’ll have a look and then make a decision before the time’s up.”