Defeat in Cardiff would mean Wales had lost all five matches in a Six Nations for the first time since 2003 - the last occasion they ended the tournament in sixth place.
Narrow losses in this season's opening rounds to Scotland and England were followed by heavier defeats by Ireland and France, leaving Wales currently four points adrift of fifth-placed Italy.
Even a win at the Principality Stadium may not spare Wales last place, should losing bonus points become a factor.
Wales No. 8 Wainwright said Friday that finishing with the wooden spoon would be embarrassing.
"We can't afford to go out tomorrow and lose," he said. "We need to win. I don't think anything else is acceptable."
Italy enjoyed a well-deserved 31-29 win over Scotland in the fourth round in Rome and were unlucky not to beat France in a 13-13 draw.
The Azzurri will now look to repeat their celebrated 2022 win at the Principality Stadium.
"Massive respect to the Italians for what they've done so far in the tournament, but we are definitely going out there and getting a win to end the campaign on a high," said Wainwright, with Wales looking to bounce back from a 45-24 defeat by France.
"We were accurate and played well in the first 20 minutes (against France), and it is about doing that against Italy and sustaining it for the rest of the game."
Wales have a miserable recent record in the Six Nations, losing 11 of their past 12 matches.
They have been hit by the post-World Cup retirements of Dan Biggar and Leigh Halfpenny - George North will follow suit after Saturday's match - and injuries to key players.
Coach Warren Gatland hailed the improving Italians.
"They look probably in better shape physically than they have ever been in the past," he said.
"They have got some depth across the whole of the squad."
