This latest league victory sees the Men of Gwent climb to seventh in the league table, 12 points adrift of the play-off places but with two games in hand.
"I'm very proud of that win, you should be proud of every win but to get four in a row is brilliant, " said Edwards.
"Consistency in performances is something we are always looking for. And after four in a row I feel we're in a position where we can challenge any one.
"With the wet conditions here we knew our forwards would be up against it. Aironi have a big pack that take some beating, they showed that against Leinster last week.
"You have to respect that and grind them down and I thought we did that. There were so many scrums and the forwards worked really hard. The back three complemented that and I thought the half-backs controlled the game really well.
The Dragons now face Glasgow at Firhill on Friday and Edwards is determined to continue building momentum as they push for a play-off place.
"Next week is another huge test, we have a four day turn around and only have one training session. It's the second of three games in a row and we have to try to carry it on."
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