"We've got a great support base here at the club," said Cornwell, who captained England U21 to Grand Slam glory back in 2006 and has spent the majority of his career with European giants Leicester Tigers.
"It's very different to most places. We've got a tiny little stadium and a really vocal crowd so it's a lot different when teams come to our home.
"There's a lot of emphasis on next week's game. Hopefully we can cause an upset at home. We just want to pick up as many points as we can and improve from last season - that's the aim."
Mogliano were unable to notch any points in their debut continental campaign last season and they conceded seven tries in South Wales in Round 1, but Cornwell is convinced they will continue to benefit from their European excursions.
Cornwell was among some senior figures who stepped back from the starting line up in Newport to hand a host of youngsters a chance to impress and the 28-year-old saw plenty of promise from his colleagues as they held the Dragons scoreless for the first 20 minutes of the second half.
And that promise is something the English centre cum fly-half has seen regularly at the Stadio Maurizio Quaggia as he enjoys his second stint at the club following a season-long return to Leicester last time out.
"We're definitely a better side now than we were in my first season. The majority of the team is still the same but the quality of the players they've recruited are a lot higher. The quality of the squad has increased over the last two years," added Cornwell.
"The Amlin Challenge Cup is definitely worthwhile for clubs like us to play. The players are always motivated to cause an upset or score some tries. The guys just want to go out and play and test themselves against good teams.
"It's definitely important if Italian rugby is going to keep getting better. We gave a game to some guys who have come through Italy U20s and if they're playing for Mogliano it can only be good for them. The guys who came in got some decent experience against some world-class players. It was a great opportunity.
"There's not too many English, Scottish, Welsh or Irish 20-year-olds get exposure in a really high level competition. They have to learn from it and I'm sure they will. They're just excited by European competition.
"Mogliano is a tiny club but they've got a really good heart and they do things in the right way. That's one of the reasons why I came back. It's a great place to be and everyone enjoys playing - that's the best thing about the sport."