Doohan recorded only the 17th-best time to become one of the first five drivers to be eliminated from the three-part session.
The Alpine pilot was on track at the time, though the clock ran down before he could cross the line and begin a final flying lap.
A delay in exiting his garage, losing him track position in the pit lane, was a significant contributing factor.
Alpine released both Doohan and teammate Pierre Gasly at the same time, the Frenchman on the right-hand side of the garage.
As Doohan joined the pit lane, he ran out of steering lock and had to be pushed back by mechanics.
While that was happening, a number of cars went by the Alpine, relegating him down the order waiting to exit the pit lane.
Gasly had no such encumbrance and recorded his best lap, a 1:28.345s that saw him progress to SQ2, as the chequered flag waved.
“It all comes down to that last flying lap,” Doohan said.
“Plan was good, feeling was good, and just ended up getting blocked on my way out of pit lane, which was a mess up specifically because it was from the other car.
“So then I wasn’t able to do the final timed lap.
“That’s why they make the length of quali that long; you do two laps and improve quite a lot in the second lap.
“I ended up being the last car out there and didn’t get a chance to do a second timed lap.”
Doohan’s only effort in SQ1 netted a 1:29.171s, leaving him 0.257s outside of what was needed to progress.
Across the garage, Gasly found 0.518s with his late SQ1 effort, suggesting Doohan likely had enough car pace to progress.
“First lap was really, really messy, just trying a few things different from practice,” Doohan said.
“Still, it wasn’t too bad, and I think there was a lot more time in the car for the second lap.
“I guess we’ll never know.”
Doohan will line up 17th for the 19-lap Sprint on Saturday, which begins at noon local time (02:00 AEST) before Qualifying for Sunday’s grand prix later in the day.
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