The Aston Martin driver was unable to take part in the second part of the shootout that determines the grid for the shortened Saturday race after sustaining heavy damage to the front-left corner.
As the Spaniard slowly proceeded through Turn 2, former Alpine team-mate Esteban Ocon was forced to correct a slide and the subsequent change of direction sent him careering into the Aston.
While Alonso crawled back to the pits with a puncture and suspension damage, Ocon shunted into the barriers to trigger a red flag ahead of a 23-minute delay for track repairs. Both drivers have been summoned by the stewards.
Two-time champion Alonso said: "Unfortunately, we could not complete qualifying. It is a shame with both cars out of qualifying and a lot of damage on both cars. Not the way we wanted [this to go].
"I've not seen the replay yet, but someone told me that he lost the car a little bit. It's one of those situations - wrong place, wrong moment."
With Aston Martin team-mate Lance Stroll 17th at the time of the red flag, and Alonso unable to run and improve upon 15th, it marked a considerable overnight downturn for the Silverstone team.
During Friday qualifying for the GP main event, a stellar Stroll lap earned him third while Alonso chalked fourth on the grid.
Alonso reckoned Aston had been left with "question marks" ahead of the sprint.
He continued: "We had great pace yesterday. We struggled a little bit more today in SQ1 to go through, so there are still some question marks on our pace.
"But I'm more confident than in Mexico and Austin, so hopefully, it will be a good race."
Stroll, meanwhile, reckoned stumbling over traffic on his final flying lap in SQ1 was the cause of his downfall.
"He said: "Just a lot of traffic on my first lap. Around here, you can't afford to be passing three or four cars on your push lap.
"That cost us a lot today. I think the car was alright. We weren't too bad. It was just a lot of traffic out there in a short session, everyone trying to do laps.
"I did my first push and my second push; I was a few tenths up and picked up a lot of traffic at Turn 7 pretty much all the way to the end of the lap. Losing tonnes of downforce in that middle sector."