The 21-year-old Monegasque locked up and ploughed into the barriers at turn eight during the second phase of an already-interrupted qualifying session after he had earlier dominated practice.
Poland's Robert Kubica had crashed his Williams at the same tight corner around the walls of Baku's old city in the first phase, forcing a 30-minute delay to mend the barriers.
"I am stupid, I am stupid," said a dejected Leclerc over the team radio, before stepping out of the car and returning to the garage.
Speaking to reporters later, he said he deserved what happened.
"I am very sad for what happened but I deserve it. I have been stupid, as I said on the radio. I have calmed down but I still think I have been stupid. This doesn't change," he said.
"I will push to learn from this and come back stronger and hopefully have a very good race tomorrow," added the youngster, who will start in ninth place on Sunday on a circuit that has been good to him in the past.
"Pole was possible today and I threw all the potential in the bin."
Leclerc, who took his first career F1 pole in Bahrain in March, said he had braked into the corner as he had done previously on the soft tyres, but he was on the mediums and they locked up.
That said, he was still blaming only himself.
"I don't want to be misunderstood. There's no problems with the tyres, it's just myself," he said. "You can definitely overtake and I will push for that tomorrow. But for the next three or four hours I will be just beating myself up."
Mercedes drivers Valtteri Bottas, on pole, and Lewis Hamilton locked out the front row in qualifying with Leclerc's team mate Sebastian Vettel qualifying in third place.
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