The Italians outscored their opponents two tries to one with scores from Brendan Williams and Ludovico Nitoglia. However Smith refused to blame his players after a narrow loss to the league leaders.
He said: "I think there is an attitude that Italian sides are negative. That we go on to the pitch to be negative.
"That's an attitude that will change if we keep winning games. We came here to play rugby, that's what we try to do every time. With so much rain it limited our possibilities to run the ball.
"We need to work on our indiscipline though. We need to finish our chances when we have them. We had the ball at the end but thought we had to do something incredible.
"We are doing the right work. I'm disappointed about the result but I am very proud of the players.
"We didn't score in the second half though. Our defence was very good and our lineout went very well too."