Michele Campagnaro twice touched down for the visitors after the resumption of play, but Gatland was satisfied by the eventual result.
"We're pretty satisfied," he told reporters. "There were some positives in our game and things to work on in terms of finishing and being clinical.
"It's a reasonable start for us and, the way Italy performed, I wouldn't be surprised if they won a few games in this competition. They won a couple last year and I think they'll do so again.
"It was tough. You've got to give Italy a lot of credit - they made it tough for us."
Wales face Ireland in Dublin in their next Six Nations outing before hosting France on February 21.