Edwards' men stormed to victory with a ruthless first 40-minute spell securing the bonus point before the break.
Former Scarlets full-back Dan Evans grabbed two tries while Andy Tuilagi and Will Harries also crossed - and after such a dominant display Edwards believes his side will be right in the mix come the end of the season.
"We hear a lot of negative vibes that come our way but we have got the making of a team that will be challenging this season," Edwards told walesonline.
"Five points, no tries against and we walk off the field with no injuries, for me that's a great night.
"There are a lot of areas to polish up on but it's pretty exciting from us at the moment and the boys finished the tries fantastically well.
"We believe these players have really got something, we just need the players to believe that as well."
Tuilagi scored the game's first try after Evans broke free as the Dragons racked up a 20-0 lead with only 20 minutes gone.
Luciano Orquera registered Zebre's only points of the match, in their first competitive outing, with two penalties as the hosts went into half-time 34-6 up, while former Ospreys and Wasps wing Tom Prydie kicked four conversions and two penalties.
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