Valencia looked well on course for their first Group H win when Michy Batshuayi put the Spanish side ahead midway through the first half on Tuesday.
Yet Guillaume Hoarau scored Young Boys' first ever Champions League goal from the penalty spot 10 minutes into the second period, and Sekou Sanogo saw a late header turned on to the post.
Despite Valencia's strong first-half display, head coach Marcelino was therefore happy to escape with a share of the spoils.
"It's tough to explain this," he said.
"Everything was in our favour to win. First half we were terrific and should have wrapped it up. Second half we were insecure, lost the ball easily and the penalty just gave Young Boys huge energy.
1-1 | Full-Time pic.twitter.com/MWD2xVoqoN— Valencia CF English (@valenciacf_en) October 23, 2018
"We have to be satisfied with the point because our opponents merited more from this game."
"It was very frustrating," added Batshuayi. "Everyone knows we came here for the three points and that isn't the case. We're very disappointed.
"Our goalkeeper was magnificent. We had to win today. It's very unfortunate."
Hoarau revelled in his moment of history but came away feeling a tinge of regret that Young Boys only drew.
"I'm very happy to have enabled the team to pick up this first historic point," he said.
"Having said that, I would have liked to have scored more goals to help the team win the game. We're a bit disappointed we didn't score another goal in the second half."