With a kinder bounce in first half injury-time, Munster would have edged ahead on the scoreboard rather than heading for the dressing room with a three-point deficit.
At that stage, having again opted to go for the corner rather than the posts, out-half Declan Cusack floted a delicate chip over the Wasps defenders only for a wicked bounce to deny the onrushing Lifeimi Mafi.
Munster were also denied a try when Peter Stringer's cross-field kick skipped out of play inches ahead of the flying Doug Howlett. That came after Ryan Davis had opened Wasps' account with a 14th minute penalty.
Tony McGahan's charges had plenty of possession and territorial advantage in an opening half that saw recent signing BJ Botha limp off with a calf injury after just 28 minutes.
They were second best on the day though, and came up against a resolute Wasps defence ably led by James Cannon, Chris Mayor and captain John Hart.
The Londoners were also sharp in attack. Replacement Billy Vunipola caused plenty of problems and Christian Wade, Jack Wallace and try scorer Varndell all threatened out wide.
It was Varndell who grabbed the decisive score in the 62nd minute wide on the right which replacement Nick Robinson converted for a 10-0 advantage.
By then, Wasps had their rearguard well organised and for the third quarter Munster's incursions into the visitors' half were rare.
Then, as the game reached its climax, Wasps were awarded a penalty at the Dolphin end, went for the corner and worked replacement Everard over for their second try.
"However, it's all part of the process of pre-season. We have got a lot of young entusiastic guys with a lot of energy out there," he continued.
"You need execution, you need skill to get results and that's something they really learned there tonight. There's no lack of will or effort out there. But you need to execute what you need to and we were off in that regard."
Last week Munster used 26 players in their away game against Stade Rochelais and again 26 got a run-out here in Cork.
Watching the Wasps game from the comfort of the new stand were Conor Murray, Ian Keatley, Damien Varley, Peter Borlase, Mick O'Driscoll and Niall Ronan.
Next up for Munster is their final pre-season friendly against London Irish next Friday at Thomond Park (kick-off 7pm). That game will be preceded by the meeting of the Munster and Connacht 'A' sides at 4.15pm.
MUNSTER: Scott Deasy; Doug Howlett, Danny Barnes, Lifeimi Mafi, Simon Zebo; Declan Cusack, Peter Stringer; Wian du Preez, Mike Sherry, BJ Botha, Billy Holland, Ian Nagle, David O'Callaghan, Peter O'Mahony (capt), Paddy Butler.
Replacements used: Stephen Archer for Botha (28 mins), Duncan Williams for Stringer (half-time), Denis Fogarty for Sherry, Dave Foley for Holland (both 47), Marcus Horan for du Preez, Denis Hurley for Barnes, Sean Scanlon for Mafi, Tom Gleeson for Cusack, Tommy O'Donnell for O'Callaghan, James Coughlan for Butler (all 52), Paddy Butler for Coughlan (60).
LONDON WASPS: Jack Wallace; Tom Varndell, Chris Mayor, Chris Bell, Christian Wade; Ryan Davis, Nic Berry; Jeremy Castex, Tom Lindsay, Simon McIntyre, James Cannon, Marco Wentzel, Richard Birkett, Jamie Harris, John Hart (capt).
Replacements used: Billy Vunipola for Birkett (20 mins), Ben Broster for McIntyre (31), Matt Everard for Wentzel, Richard Haughton for Wallace, Charlie Davies for Berry, Nick Robinson for Davis (all half-time), Nathan Morris for Lindsay (45), Bob Baker for Castex (52), Alex Cheesman for Mayor (62), Guillermo Roan for Broster (68 mins). Not used: Jonah Holmes.
Referee: Dudley Phillips (IRFU)