And the bonus-point win was secured thanks to tries from Dominic Waldouck, scrum-half Joe Simpson, Tom Varndell and Ben Jacobs getting on the score sheet for Wasps.
Ruaridh Jackson led the charge for Glasgow contributing 19 points, including a try, but it wasn't enough and Lineen said: "We just hung off them. They weren't doing anything too special just being very direct.
"But it is a bonus point victory to Wasps and we aren't very happy with that. I thought we had a pretty poor first half collectively, especially those first 20 to 25 minutes and that killed us.
"The tries we conceded were too soft but we did show more spirit in the second half and scored a couple of tries ourselves."
Meanwhile Edinburgh suffered a similar fate losing 31-27 to Northampton - who now move top of Heineken Cup Pool One - at Murrayfield.
Tries from Edinburgh trio Allan Jacobsen, Netani Talei and Ben Cairns were cancelled out by scores from England international Dylan Hartley, James Downey and Paul Diggin.
But it was the penalty count that cost Edinburgh with Stephen Myler kicking four to Chris Paterson's two as well as two conversions.