Former England and British & Irish Lions star Dallaglio though, believes the game is already up, with Wasps the only team yet to record a win in Pool Six, a group they currently prop up after claiming just three points.
Wasps had to beat the Scarlets at a fog-shrouded Stradey Park, but they collapsed 21-13 as Llanelli scored second-half tries through centre Dafydd James and wing Mark Jones, while fly-half Gareth Bowen kicked 11 points.
After winning the competition in 2004, Wasps are now poised to make a second successive pool stage exit.
"I am very disappointed and very angry with everyone, including myself," said Wasps skipper Dallaglio. "With the quality in our group, it was going to be very difficult, but we just weren't good enough.
"We are trading on our reputation of the last two or three years, and we have got no divine right to win any game.
"It is down to hard work, effort and energy. At the moment, one or two are putting it in, and one or two aren't."
Substitute flanker Tom Rees scored a late try for Wasps, but Alex King missed two of his four penalties and the visitors made no real headway against a Llanelli pack inspired by the scrummaging power of veteran prop John Davies.
"We were nowhere near the standard we want to be at, and our worst two away performances this season have been in the cup," said Wasps rugby director Ian McGeechan.
"We are really annoyed with ourselves, but we will be full-on in the next three European games and we intend to hurt a few people if we can."