But the versatile play-maker insists Wales still have some harsh lessons to learn and must improve ahead of welcoming Ireland to the Millennium Stadium.
"We expect more from ourselves, but the main thing was the win," said Hook.
"There were a couple of steps forward. The performance wasn't great, but it's a win… and two wins from two on the road is big for us. We can build on that.
"We expect more from ourselves, but the main thing was the win. We sat down and had a chat in the changing room afterwards and I think we were happy with the result in the end.
"There were a few negatives in our game. We probably should have held on to it in our 22, we chucked silly passes away and had a few turnovers.
"We've also got to hold our hands up and admit we've been struggling with discipline over the last couple of campaigns. We've got to cut that out of our game because we're letting sides back in, especially away from home.
"Against Italy you're not going to score tries from anywhere. The penalties is what they live off and they'll kick three, six, nine points and keep themselves in the game.
"But it's always tough out here. A lot of the boys have played out here for the last couple of years and we know how hard it is to win out here.
"So the win was important and hopefully against Ireland we can build on that, put a better performance in and try and get a win.
"We played within ourselves in the second half because we were hanging on to our lead. We didn't want to leave Italy back into it.
"We know what sort of side they are - they can score tries from anywhere at home.
"I think we deserved the result. Italy battled hard, especially in the second half, but I think our first-half display was pretty good.
"We held on to the ball and if we'd done that in the second half we would probably have run away with it. There's obviously a lot to work on, but we definitely deserved the win."
Hook made six appearances for the Lions during the 2009 tour of South Africa and amassed 35 points.