The 37-27 setback saw the Londoners slip from first to third behind Munster - 29-19 conquerors of Llanelli Scarlets - and Clermont.
It was Wasps' heaviest Heineken Cup loss since Stade Francais crushed them 31-0 in 2002, and a first tournament reversal in 10 games stretching back more than 13 months.
Skipper Dallaglio said: "This is a really tough pool, and I am disappointed we didn't manage to pick up a bonus point.
"But now we have to do the business at home next week."
Wasps were finished off by a contentious Mario Ledesma try, awarded despite his grounding of the ball proving inconclusive.
But Dallaglio added: "What I think about the Ledesma try is irrelevant, but it goes both ways.
"Sometimes you get those decisions and sometimes it goes to the opposition. I was more disappointed with the way we gave away first-half tries.
"Now, it sets up the match next week nicely, and it will be a real contest."
Munster, edged out by Wasps on the competition's opening weekend, overcame appalling Stradey Park conditions as 19 points from fly-half Ronan O'Gara effectively ended Llanelli's quarter-final hopes.
Even a violent hailstorm could not blow Munster off course, leaving last season's semi-finalists Llanelli still without a point after three games.
Leicester prospect Jordan Crane further enhanced his reputation with a man-of-the-match display in Tigers' 14-9 victory over Pool Six rivals Toulouse.
The 21-year-old number eight delivered an irresistible display, underlining why many astute judges feel he could break into England contention this season.
Tigers wing Ollie Smith scored the solitary try of a fiercely-fought contest, although Toulouse's bonus point keeps them in pole position above Leicester and Leinster.
Crane said: "We dogged it out, and it is going to be a real test when we go over to Toulouse next week.
"Nothing other than a win will be good enough for us, and that's what we are going to try to get."
Bristol followed up an impressive demolition of French champions Stade Francais by staying firmly in Pool Three contention with a 17-3 success at Harlequins.
Tries by Alfie To'oala, David Lemi and Luke Arscott saw Bristol home, and head coach Richard Hill said: "We've won two games now in the Heineken Cup, and that is probably two more than we expected."
Hill reserved special praise for hooker Mark Regan, back in the side after ignoring his club's pleas to rest last weekend rather than skipper the Barbarians against South Africa at Twickenham.
Hill added: "His attitude was superb.
"I could tell he was up for the game. In the hotel and in the dressing room he was pumped up, and he got the rest of our pack going.
"I am convinced now that it is well behind him and his head is back on Bristol."