The Leicester City legend was also named the official man-of-the-match.
Vardy said on DAZN: "I think we're coming out of a difficult period, and this would have been a typical midweek game in Italy.
"It's nice to score two goals, but the most important thing is to get the three points and maintain this progress. This is another step in the right direction.
"Yes, there was a very British rainy week, but the key thing was to get the three points and, above all, take another step forward."
It was also put to Vardy that his Cremonese teammates have highlighted how he never complains. Asked if he's noticed a difference with the moaning of Italian footballers, Vardy was diplomatic.
"No, not really. At the end of the day, my teammates don't complain when we're at training or in other situations. Everyone is committed and wants the best for the club.
"Everyone is on the same page and pushing to ensure we have a successful year at the end of the season. No, I haven't actually noticed it because at least in the group, everyone pushes 100% to achieve a single goal with great humility and, above all, to get to the end of the season."