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O'Connor was involved in a crash which saw four to five riders go down in the peloton with just under 40 kilometres to go on the longest stage of the 2023 Tour de France.
While the Western Australian arrived safely back in the peloton a short time after, the crash dealt a major blow to his GC prospects, having already lost time the previous day after being dropped on the final climb.
The AG2R Citroën Team leader eventually crossed the finish line in a bunch 58 seconds behind stage winner Victor Lafay (Cofidis), falling one minute and 41 seconds behind overall leader Adam Yates (UAE Team Emirates) in the general classification.
"It's a hard day, we expected a different result," AG2R Citroën Team general manager, Vincent Lavenu said. "We expected to get one or two riders in the main group.
"Ben O'Connor was alright until the last 500m of Jaizkibel and then got dropped.
"He was 20 seconds behind and never came back. He's disappointed, we're disappointed. I know that the team can bounce back."
Meanwhile, Hindley remained firmly in touch with the rest of his GC rivals after finishing the second stage in ninth place, dropping only one position in the overall standings, 22 seconds behind the yellow jersey.
"Today was just about following and conserving energy," Hindley told SBS Sport's Gracie Elvin after the stage.
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"It's only day two, so I was just trying to save myself as much as possible and just not lose time on the big favourites, and we did that so I think we can be happy.
"The boys (teammates) did another great job and the support's really incredible. So, all going good so far."
Jack Haig (Bahrain-Victorious) worked his way up the overall standings after finishing safely in the leading bunch alongside teammates Mikel Landa and Pello Bilbao, speaking after the stage of how he saw the finish pan out.
"(On) the final climb, UAE (Team Emirates) obviously had quite a big plan there to try and take the bonus seconds at the top," Haig told SBS Sport.
"They never really let the breakaway get too far away and they set a really, really hard pace.
"We were just behind in a group with me and Pello and Mikel. We worked a little bit across the top to make sure that we brought back (Tadej) Pogacar and Jonas (Vingegaard) and then Pello had a bit of a try on the downhill.
"But Jumbo-Visma were there with quite a few numbers and brought it all back and then finally, the Cofidis rider (Lafay) took it from them in the finish."
The Team DSM Aussie quartet saw their French leader Romain Bardet finish in the lead bunch, with Sam Welsford commenting on the length of the sprint finish.
"We were in good position before the intermediate sprint, and I looked back to the guys and I asked them if I could have a little crack just to open up the legs and see how they're feeling," he said.
"I had actually had a good sprint. It was a really fast and these intermediates, they always kick off from 500 (metres) to go.
"It's a really long sprint so you have to time it well, and yeah, it was alright."
Lotto-Dstny sprinter Caleb Ewan had his sights set on tomorrow's first sprint stage of the race after expressing mixed feelings about his performance on Stage 2.
"Well, I didn't know whether I was gonna go for it (the intermediate sprint) today or not, but I ended up getting there," he said after the stage.
"But yeah, in the end I chose the wrong train to go with on the left side and I didn't even know why I came there. It wasn't really a test drive of the legs, but I feel good - I feel like I was climbing pretty well.
"So, hopefully tomorrow is a good one."