Dragons wing Gareth Wyatt was on Cipriani's shoulder, trying to prevent the score but went flying as the Wasps man went over.
Richards, on advice from television match official Tony Rowlands, however, disallowed the try because Wyatt had been illegally pushed out of the way.
But Wasps director of rugby Ian McGeechan and head coach Shaun Edwards were livid after the match, claiming the referee was not at liberty to ask for advice from the TMO.
McGeechan said: "It was in the field of play and he is not allowed (to ask for the TMO's advice) in the field of play on anything. The referee or touchjudge should do that.
"It's disappointing because we are pretty certain this has been done in the field of play and not in the try area (where he could ask for the TMO's help)."
Edwards was equally furious and said: "We've looked at the rule book and there is nothing to say they can do that. If it was foul play inside the field of play, he is not allowed to do it."
The match itself was dour, but McGeechan said: "It was important for us not to lose here tonight. Credit to both sides and their workrate and attitude. It was first class in the conditions."
The drizzle and the mistakes, which saw no less than 51 scrums awarded with 19 of them having to be re-set by the referee, was mostly responsible for the dreary fixture between the Welsh region and the Heineken Cup champions.
But Dragons head coach Paul Turner was upbeat about his side's display. Turner said: "We talked about it during the week that we wanted to beat the European champions because that was our yardstick.
"You have to take your hat off to everyone on both sides for the physical contact of the match. It's give us another pointer to what we can expect in Europe. I feel both sides made too many errors but some of the hits in the match were top rate.
"We cocked the gun but we were not able to pull the trigger to win it at the end."