Stand-in captain Dan Lydiate says Wales owed it to their fans to end their Six Nations campaign on a high.
"We are still disappointed with last week and we owed it to the fans," Lydiate said.
"We still gave away some soft tries but the boys played their hearts out and I couldn't ask for anything else from them."
Lydiate, deputising for regular captain Sam Warburton, says Wales must learn lessons from the campaign.
"Two bad halves of rugby let us down in this championship and let's hope we learn from that and we never start again like we did in the first game and against England," he said.
Replacement Ross Moriarty ran in his first two Six Nations tries after coming on as a replacement.
"Two tries, I couldn't ask for anything better for myself," the Gloucester flanker said.
Fast start pleased Gatland
Head coach Warren Gatland was happy to see Wales learn lessons from their slow start at Twickenham.
"We spoke about how important it was to go out and start better this week and in fairness to the players they did that," he said.
"They stood up and I was hugely impressed with the the way they responded to the disappointment of last week in terms of taking that responsibility and we put that behind us and focused on today and finishing second."
Gatland praised man of the match George North for his display in a game where he carried the ball 143 metres and scored his fourth try in as many successive games.
"He's started to play with a smile on his face and with some confidence and he's probably getting back to where he was in 2013," said Gatland.
"He's in a really good place at the moment and we can build on that and we're pretty excited about the summer."
Justin Tipuric, who was replaced by Moriarty in the 15th minute after suffering a blow to the head, will spend a night in hospital for observation, and may miss Ospreys' Pro12 match against Scarlets next Saturday.
Gatland said: "Justin Tipuric has been taken into hospital tonight but only as a precautionary measure so should be all right."
The coach was pleased with Moriarty's contribution, saying: "I thought he was outstanding. Ross Moriarty made a great impact when he came on and we know that he offers us something different."
Wales won by a record margin of 53 points against the Italians, whose captain Sergio Parisse was full of praise for Gatland's side.
"We lost against a great team in Wales which shows the young guys must work on this defeat and get better for future," he told BBC Sport.
"The campaign was really difficult. Every team gets injuries but for us it is maybe much more difficult because we don't have the depth. But no excuses, from June we have another staff and maybe things will change.
"It is difficult to play matches when you lose by 50 points but there was some good things. We scored two tries but there were too many mistakes in defence. They have great players, great backs and put us under pressure today."