It was the first time in 67 races that Hamilton has not made it into the final part of qualifying.
Lewis Hamilton 'drove like an idiot' in Italian GP qualifying
Hamilton - who has been on pole for the last four races - ran wide out of the fast final Parabolica corner and bounced over the gravel on his first run in the second part of qualifying, but he blamed himself for the failure.
"I drove like an idiot," Hamilton said. "It's the worst I've driven for a long, long time. I'm just sorry for the team."
Asked if Force India's Adrian Sutil had impeded him at Parabolica on his final lap, Hamilton said: "Yeah, but I should have done it on the previous lap. I just didn't drive well."
BBC F1 co-commentator David Coulthard said: "It's great he is so open but I feel for Lewis when he is so hard on himself. He is a great driver and he has had a great start to his Mercedes career."
BBC F1 technical analyst Gary Anderson added: "Sergio Perez qualified outside the top 10 [also in 12th] for Sauber last year and came through to second. There is no reason for him to be so down on himself. Today is over. It's about tomorrow now."
Not since the Malaysian Grand Prix in 2010 has Hamilton failed to make the final part of qualifying - 67 races ago
Hulkenberg put Sauber into the top 10 for the first time this season with a sensational performance - and at the perfect time, as he is one of the drivers in the frame for a Ferrari drive next season.
Sauber team principal Monisha Kaltenborn said: "We couldn't believe it ourselves. We were hoping to be a bit further up than P10 but this was a surprise, it was a fantastic lap and he did a great job."
Hulkenberg said: "I dunno [where it came from] either. It was a nice surprise. We didn't expect that after a difficult Friday. The team worked really hard and the car just got better and better, and it was the right decision to just go for one timed lap."
Ferrari had attempted to get Alonso on to the front row by running Massa ahead of the Spaniard on all his qualifying laps in order to try to provide a 'tow' - a boost of straight-line speed because of reduced drag.
But starting his final lap Alonso, who had been second to Vettel in the second part of qualifying, complained over the radio that "Felipe is too far ahead".
However, the paper also notes the similarity between the words for "genius" and "idiot" in Italian, and notes that some people heard him say "geniuses", presumably ironically.
Despite that, two thirds of the way around his final lap Alonso was only fractionally slower than Vettel's benchmark time from the German's first run, but then seemed to lose out in the last sector and Massa was able to sneak ahead of him.
Mercedes driver Nico Rosberg took sixth ahead of Toro Rosso's Daniel Ricciardo, with the McLarens of Sergio Perez and Jenson Button eighth and ninth and the second Toro Rosso of Jean-Eric Vergne 10th.
Sutil was later given a three-place penalty for impeding Hamilton, dropping him to 17th and moving team-mate Paul Di Resta up to 15th.
Sunday 8 September: Race coverage at 12:10 BST on BBC One & BBC Red Button at 13:00 BST, plus Radio 5 live at 13:00 BST, and live text commentary online. F1 Forum, 15:15 BBC Red Button. Highlights, 19:00 BBC Three & BBC Red Button
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.