A Sergio Parisse try brought the Azzurri to within five points in the second half but Gatland was delighted with the way his side held their nerve to make sure of the win.
"We showed a little bit of composure there and a bit of professionalism that we haven't sometimes in the past achieved," he said.
"I think we were under a bit of pressure at the end there and we dug deep so that's probably for me the most pleasing thing.
"We made it hard for ourselves by gifting them a couple of tries. I thought the one that the touch judge called for the forward pass was very unlucky - I thought it was there.
"In particular they've got a very strong scrum and we probably tried to play a little bit too much rugby in the first half rather than get the go-forward.
"You try and play a bit of rugby and you've got to look at the scoreboard as well so that you get the win and get the result, but we've made it tough for ourselves."