The Australian, last year's winner in Baku, had lined up ninth after crashing in Saturday's qualifying but dropped to last after jumping the start.
He then locked up and smashed into the wall at turn five, ending his streak of 34 successive finishes and scoring in every race this season. By the end, his lead over teammate Lando Norris was slashed to 25 points.
"Certainly not my finest moment," the 24-year-old told Sky Sports. "I just anticipated the start too much and yeah...silly simple error really.
"The crash, I just didn't anticipate the dirty air in the way I should have and clearly went into the corner way too hot and that was that.
"I'm certainly not blaming it on anything other than myself. Just didn't make the judgement calls that I needed to at the right time and that's obviously a disappointment."
Piastri's lead cut to 25 points
Piastri had gone into the race with a 31-point lead over Norris, who started and finished seventh.
McLaren had hoped to clinch their second successive constructors' title, and 10th in their history, with seven rounds to spare, but that will now have to wait until Singapore in two weeks' time.
Piastri has barely put a wheel out of line all season, apart from running wide in his home opener in Melbourne and finishing ninth, but Baku was the weekend it all went wrong for the man hoping to become Australia's first champion in 45 years.
He also collected a five-second penalty for the jump start, which he was unable to serve.
"Friday was a tough day, I think Saturday the potential was very good...I had a lot of sequences or sectors that were incredibly strong and just never got it all together," he said.
"And then today, just more silly mistakes. So yes, it was certainly a messy weekend.
"But I would be more concerned if I was slow and trying to make up for it that way and causing and having these errors because of that.
"The fact that they're just simple lapses in judgement...it's obviously not a position I want to be in or put the mechanics in because it's been a rough weekend for them but if I'm trying to find a silver lining then I suppose I have that," he added.
Piastri, winner of seven of the 17 races so far, played down the impact of one round on the championship, saying there was still a long way to go and he was focused solely on his own performance.
