Norris qualified just 17th fastest after aborting his final lap of the first segment of the three-part session.
The McLaren driver slowed on the long front straight as Pierre Gasly limped his wounded Alpine back to the pits with the left-rear puncture.
The Frenchman had tagged the wall half a lap earlier as the pack wound up for its final run in Q1.
Keeping out of the way, he cut across the apex of Turn 16 and remained on drivers’ left shortly before Norris arrived on the scene on a flying lap.
“Just the guy ahead of me crashed and there was a yellow flag,” Norris reasoned after qualifying elimination.
“When you have a two-kilometre straight, and you need to lift off at the beginning… Nothing I could do, honestly,” he added.
As Norris exited Turn 15, a yellow flag panel was illuminated on the approach to Turn 16.
LED panels hold regulatory value in F1, meaning the illuminated board is the same as a yellow flag and Norris was obliged to obey it once he arrived at that point on the circuit.
However, onboard vision from the McLaren shows it was switched off before Norris got there.
He then went deep at Turn 15, riding the exit kerb, passing a white flag being waved by a marshal.
Norris then slowed as he passed Gasly, abandoning his lap shortly after to cement his exit from the session.
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It left both driver and team frustrated, the latter questioning the FIA about it incident.
“We were discussing now with the FIA as to why a yellow flag was displayed at that moment in time, which was extremely, extremely costly in the economy of this weekend,” said McLaren boss Andrea Stella told Sky Sports.
“The yellow flag isn’t necessary when it’s just a slow car,” he added.
“Everyone tries their best, I’m sure, this time there was a situation which ideally, and I think by the regulations, shouldn’t have happened.”
The incident was especially costly as Norris is the nearest challenger to Max Verstappen in the drivers’ championship.
The pair are split by 62 points heading into Sunday’s race, with Verstappen qualifying sixth fastest.
“I’m still hopeful we can get a good result,” Norris told Sky Sports.
“The car’s quick, I think the lap I was on actually could have gone second, so a bit frustrating but nothing I can do.”
The Azerbaijan Grand Prix begins at 21:00 AEST.