"It's a high-profile competition and we need to do well to improve the brand. We're a region that have drawn a line in the sand and want to move forward," said Jones.
"Results and performances on the field are very influential in how quickly the business can repair itself from things that have gone on in the past four or five years off the field."
The Dragons and Mogliano are joined by Bath and Bordeaux-Begles, who meet in France on Saturday night.
However, the home side will be expecting maximum points from their opener, having recorded a double over Mogliano in last season's competition with 53-3 and 33-0 successes.
And, while Jones believes his men are in the toughest group, the ex-Ospreys and London Welsh coach reckons the Men of Gwent can quality for the latter stages of the tournament.
"It's going to be a tough group and it'll be tight between Bath, ourselves and Bordeaux-Begles. It will probably be the toughest group in the Amlin Challenge Cup,2 added Jones.
"If we can be in with a shout and in charge of our own destiny in Rounds 5 and 6 then we'll be confident that we can get through. For the credibility of the business, we need to perform well and get through to the quarter-finals."