Edwards admits the defensive lapses in Biarritz were unacceptable and he has urged his side to improve in their latest pre-season outing at Rodney Parade.
"The biggest disappointment against Biarritz was that four of their six tries came from clean line-breaks from set-pieces," said Edwards.
"If a team breaks you down with a multiple-phase attack and good play then you have to accept it, but not first-phase play.
"It was down to new combinations and system errors. That can happen at this time of pre-season, but we cannot accept it against Zebre in two weeks time.
"Hopefully we've identified those areas and will put things right against London Irish.
"I don't want us to be giving away soft tries and I want us to look a tough team.
"But testing ourselves against a top European team like Biarritz was a valuable exercise and there were some pleasing aspects.
"The attitude and focus at the breakdown, something we have worked hard on, was excellent and we turned them over 12 times.
"The games against the Gwent Select and Biarritz came after we had stressed our squad with very hard, physical training.
"But I want an intense performance this weekend. The training is tapering off so the fatigue levels are dropping and I want a display that gives a picture of what is to come."
Hooker Steve Jones continues to lead the side in the absence of regular captain Lewis Evans.
Meanwhile Dan Lydiate and Toby Faletau are set to make their first appearances for their region, following their exploits during Wales' summer tour of Australia.
Dragons: D Evans; M Pewtner, A Hughes, P Leach, T Prydie; Steffan Jones, W Evans; P Price, Steve Jones (capt), N Buck, I Nimmo, A Coombes, D Lydiate, D Waters, T Faletau.
London Irish: T Homer; T Ojo, J Joseph, J Ansbro, S Tagicakibau; S Geraghty, T O'Leary; M Lahiff, S Lawson, L Halavatau, B Evans (capt), M Garvey, A Gray, J Fisher, O Treviranus