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Grosjean suffered the bizarre elimination while attempting to keep his tyres warm during the latter stages of the race, losing the rear of his car and finding himself in the barriers.
Up until that incident, the Frenchman was running in P6 – an impressive showing given he started the chaotic Grand Prix at the very back of the grid - and he had been enjoying a tussle with Sergio Perez, who went on to finish third with Force India.
“This hurts a lot and I want to apologise to the team," said a gutted Grosjean. "We were in the middle of an amazing race, starting last and running P6.
"Seeing (Sergio) Perez on the podium, knowing I was fighting with him, is very painful for all of us. It was going very well."
Grosjean said 'conditions were tricky' on track but offered up another explanation for his embarrassing error.
"There was a lot of wind, the car was going left and right, pushing then not pushing," he explained.
"I was warming up my tyres and bumped into a switch that I’d moved by two positions. When I touched the brakes, the brake balance was locked rearward – it just locked the rear wheels and I spun.”
It was a miserable finale for Grosjean, who would have collected a morale-boosting eight points for Haas had he held on to his sixth spot.
“It's always hard when you lose so many points and obviously when you crash under the Safety Car," he added.
This latest disappointment means Grosjean remains P19 in the drivers' standings and is still without a single point this season, while his team mate Kevin Magnussen has collected 11 thus far.
The Dane, however, also left Baku empty handed after getting a 10-second time penalty for a late clash with Pierre Gasly.