"That victory in Scotland won't mean anything if we don't go on and get another win in Rome," Byrne said.
"We have come unstuck against Italy before, and we must definitely have our game heads on. It's all about learning the lessons of the past and realising that Italy are improving year on year.
"They are a force at home. It's like a club ground the way the spectators are very close to you. It is smaller than most other international arenas, and the atmosphere is quite intimidating.
"They do raise their game and get the most out of their players. Yes, they had a heavy defeat against England, but on the back of that defeat they will be looking to put things right.
"I don't think the beating they suffered at Twickenham will help us. Their match with Ireland in Rome, when they lost by two points, was more of a reflection."
Wales ended an eight-Test winless streak with their success in Scotland, and Byrne expects another victory if they can repeat that display.
He added: "If we can repeat that sort of performance in Rome then Italy will find it difficult to live with us.
"There is more of a spring in the step now we've got the win we had been searching for. We had been trying so hard to get it and put things right, and now we have, everybody is more relaxed."