Captain Alun Wyn Jones said Wales had their “foot in the door” after getting their Six Nations campaign off to a winning start.
Rob Howley’s men saw England and Scotland record victories on Saturday and the Dragons responded with a 33-7 win over Italy in Rome.
But they will need a considerable improvement to threaten next Saturday’s opponents England following tries during the final quarter from centre Jonathan Davies and wings Liam Williams and George North as they posted 30 unanswered points in the second period.
Full-back Leigh Halfpenny kicked 18 points as Wales reeled off an 11th successive victory over the Azzurri, who struck first with an Edoardo Gori try that fly-half Carlo Canna converted.
“The first half proved how much of a test it was,” Wales’ new captain told ITV.
“We started slowly but the character showed. We got our foot in the door after the way results have gone.
“We worked a little harder, kept the ball and we came together in the second half. We will stay on message.
“We are a day behind everyone else so it is a foot in the door.”
North added: “I think, the first half, the weather came down and it was going to be a tight game anyway.
“We had to fight to the end, every inch, but we’re happy with the performance.
“We know they are a passionate team but we backed ourselves and it showed.”
Conor O’Shea says he wants to see Italy “refereed on a level playing field.”
The former Harlequins boss, now Italy’s coaching director, struggled to mask his frustration after Wales cut loose in the second-half to score 30 unanswered points.
Of as much concern to the Irishman was a 16-5 penalty count against his team, and he feels the Azzurri need to change what he believes is a perception about them.
“Rugby is a rollercoaster,” said O’Shea, who made no specific mention of match referee JP Doyle. “Energy comes in different ways in games, and we’ve a big challenge to change a lot of our mentality and to understand that things do go against you. We lost our discipline in the second half.
“The energy being given the whole time to Wales meant it was very difficult for our team to stay on task as they did in the first half, when they were magnificent at times.
“We have to change perception because we need to make sure both red and blue are looked at in exactly the same way. We know that Wales were the better side in the end, but I thought we were better in the first half.
“We have to make sure we change the perception of people who look at us, so we are refereed on a level playing field. The energy that is driven away and towards an opposition is huge when it is 16-5 (penalty count).
“We have a huge, huge challenge. I want to make sure we are looked on the same as others, and then we will be fine.
“Our defence in the first half was amazing, so there is lots to be positive about, but we can’t lose a penalty count 16-5 and win matches.
“We will look at ourselves first. It’s our fault. We will look at what we control, not anyone else, but human nature is human nature and we have to change a perception that people have, not today, but all the time.
“We have to be whiter than white and look at ourselves and what we can do better, not get frustrated when decisions do against you.
“We are probably talking too much about the referee now. It is just one of the many things that we have to get our heads around.
“I have no doubt that the penalties given against us were probably right, but only five were given against Wales. Watch the first two minutes of the match and the scene is set.”
Wales coach Rob Howley said: “It’s a win. Momentum is important in the Six Nations as a tournament. I thought the composure that we showed, particularly at half time, I think you saw the experience of the team.
“The majority of this team were here two years ago when it was 15-14 and we know how tough it is to come to Italy. [But] we want to improve in all areas.
“We use the word relentless, with and without the ball. There were aspects of our game today when we weren’t relentless with the ball. We have to put England under more pressure than we did Italy.”