Fly-half Danny Cipriani pulled the strings as Eoin Reddan, Tom Voyce and Paul Sackey ran in tries but Wasps then took their foot off the pedal.
Clermont hit back through Aurelien Rougerie and Filimoni Delasau with substitute Emmanuel Etien barging over four minutes into injury time to secure the bonus point.
Wasps' Lawrence Dallaglio said: "We played 40 minutes of outstanding Heineken Cup rugby - the best we've played in a long time against a good side - and then played 40 minutes of the worst rugby I've seen.
"We blew four tries in the second half and also gifted them two tries.
"Often when you're going for bonus points you think you've got the game won.
"It now looks like we'll have to win our last two games to qualify.
"This group had last game written all over it and that's how it's proving."
Wasps director of rugby Ian McGeechan was angered by Julien Malzieu's deliberate knock on when Wasps were camped on the Clermont line.
The European champions were 25-17 ahead at the time and McGeechan felt they should have been awarded a penalty try.
He said: "We've had two rough decisions in two games and it's disappointing.
"It's swings and roundabouts but we're still waiting for the roundabout."