The Norwegian has been the nearly-man of this year's Tour, finishing second in two stages and third in two others.
But losing out to Australia's Michael Matthews in the latest stage was particularly frustrating, given the significance of the day for the African continent's only World Tour team.
"This was a really hard stage. The team did very well to keep me at the front all day," he said after wind had made the 165km trek to Romans-sur-Isere such a tough day in the saddle.
"Everybody did such a great job. Unfortunately, in the last corner, I was a bit too far down.
"I knew I had to be at the front at that point but sometimes these things happen. I was probably the fastest rider on the last stretch and I almost made it.
"It's a shame. This was a good chance for me."
The team, then known as MTN-Qhubeka, won a stage on Mandela Day two years ago on their Tour de France debut when Steve Cummings took stage 14.
This year, the team suffered a huge blow to its chances of winning a stage when Briton Mark Cavendish, the Tour's leading active stage winner, withdrew from the race after a crash on stage four.
The Dimension data team races to raise funds for the Qhubeka Charity, which provides bicycles to people in Africa.
(Reporting by Martyn Herman; Editing by Christian Radnedge)
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