"We had a job to do and we went out and did it," said Wallace. "It was a very physical game. It's good to get a win under our belts.
"In fairness to Italy, they never gave up. Of course you want to score more tries but that would be a disservice to Italy."
Jamie Heaslip and Tomas O'Leary scored first-half tries for Ireland as they established a 23-3 lead.
Fly-half Ronan O'Gara finished the game with 16 points on his return to the side while Italy's only try came just before the break through Kaine Robertson.
O'Gara took a bang on the knee in Saturday's game but Kidney expects the fly-half to be available for the game in Paris.
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