But Glasgow can take great heart from running the English champions close for an hour before the visitor's extra class and experienced finally told with three late tries.
Such was the level of expectation for Glasgow's first European Cup outing at the Scotston Stadium that the kick-off was delayed for 15 minutes to allow the 3,500 capacity crowd in.
The visitors struck first with two penalties from their full-back, Gareth Rees, but Glasgow's Cook Islands' stand-off, Tommy Hayes, put the home side on the board with one of his own.
Chris Sheasby made the first try of the game when he broke from the base of a scrum 20 metres out before slipping the ball to Andy Gomarsall.
Rees's conversion made it 16-3 in Wasps favour after 23 minutes, but Hayes pulled Glasgow back into the game before the half-hour mark.
Intercepting a Gomarsall pass on the halfway line he galloped away to score in the left corner but Sheasby replied with a pushover try which Rees again converted to give Wasps a 23-8 half-time lead.
Glasgow continued to run the ball from all positions and after Derek Stark made 50 metres with a powerful burst down the middle, quickly recycled ball allowed Hayes to dive over for his second try.
Glasgow's resistance crumbled however and tries from Greenstock, Logan and Shane Roiser in the last 10 minutes gave the winning margin a slightly flattering look.
Gordon Bulloch gained some consolation when he drove over for a third try on the whistle.
"We expected it to be a difficult game," Nigel Melville, the Wasps director of rugby, said. "But it wasn't one of our best performances."
The Glasgow team manager, Hamish Fyfe, felt his side had made too many mistakes but was pleased at their general progress.
"We had a lot of young, inexperienced boys out there today and I think some of them were a bit in awe in the first 20 minutes.
"But in a month's time I think you will begin to see the difference full- time rugby will make. I think you will see an improvement next week against Swansea."
Glasgow: Tries Hayes 2, Bulloch; Conversions Hayes, Little; Penalties Hayes. Wasps: Tries Gomarsall, Greenstock, Logan, Roiser, Sheasby; Conversions Rees 3; Penalties Rees 5.Reuse content