Dimension Data took control of the race in the final five kilometres to attempt to set up Cavendish for his 31st career win in the Tour and first since 2016. However it was Fernando Gaviria who came through with the benefit of his Quick-Step Floors. Peter Sagan (Bora-Hansgrohe) placed second.
"The team was brilliant," Cavendish said at the bus. "For the last kilometres, it was actually what we wanted. We executed how we wanted in that headwind."
Cavendish spoke while holding his new baby boy Casper while his team-mates, including lead-out man Mark Renshaw, warmed down behind him.
"With a block headwind, once you weren't in the wheel, your watts went double. I think [Søren] Kragh Andersen came in and pushed me out of Renshaw's wheel, so it was better to go on his wheel than to be in the wind.
"I thought, 'OK, he'll go.' He started to go around Renshaw, then Renshaw started lead out and then I thought 'the left would be closed'.
"Then a gap opened on the left, Quick-Step went on the left, and I was blocked by my own lead-out man. That's going to look s*** on paper.
"It was my own fault, I shouldn't have really been there. They've gone with the stage win and I'm left here holding a baby."
The mood around Dimension Data improved on Tuesday, after four stages of the 2018 edition. Cavendish was left behind in the first two sprints and waited until stage four, after Monday's team time trial, to have another go.
The South African team contributed to the pace-setting throughout the stage and led into the final kilometres Thankfully they avoided the carnage of a crash that rocked the pack with around five kilometres to race.
"That's what we want to take from it," sports director Roger Hammond responded when asked if the team is gelling and Cavendish is improving.
"We wanted to be aggressive and take it by the horns, they did that. It's only the last 300m they had an issue.
"What's the ultimate thing? You have to get your sprinter in a place to sprint, we got that. I haven't talked to Mark to see what he felt there. We haven't had a full debrief yet."
Cavendish left the 2017 Tour de France with a broken shoulder blade, and he has already crashed three times in the build-up to this years race, suffering fractured ribs in the process.
"He's had to pick himself off the ground a lot. He's getting better," Hammond said. "Was he good enough to win? Yes, we think so. That's the whole point with Mark, he's going to be more likely to win later, he's on the way up fresh, where a lot of people have done racing so far."
"It was a better performance than stages one and two," Dimension Data general manager Doug Ryder said. "When we didn't have it together, we kind of got boxed in and lost each other.
"He's a champion and you don't write off a champion. He's earned that status and he's living it. You never kick a dog when it's down or it will bite you.
"I think Mark's got it mentally and hopefully as he gets through this race, he can get better and better. He's leaner than he has been for a while and looks good. He's just lacking a little bit at the moment."
The next two lumpy stages leaves Friday as Cavendish's next chance to sprint for a stage win, and hope that the softening up process of the hilly stages of Wednesday and Thursday might improve his chances.
"We'll see what's happened," Cavendish said of Friday. "The Tour's hard tomorrow, isn't it? We will get through, a few of the sprinters will have more tired legs.
"Like I've said, we've come here a little up against it, but we'll keep trying."
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