Robbie Brady's 85th-minute header put the Republic into the last 16 of Euro 2016 as they beat the Azzurri 1-0.
O'Neill's side top their World Cup qualifying group, with Wales third.
"There is a distance to go. By the time the game is done we're halfway through the campaign," O'Neill said.
Referring to the Italy game, he added: "It's not a distant memory. Some of the players who performed that evening can call upon the experience again and go for it.
"I think we will have to produce a performance like that against Wales. I think the players are ready for it."
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The Republic drew against Serbia in the opening game of their qualifying campaign but have since beaten Georgia, Moldova and Austria.
"We've got 10 points on the board and three games away from home but naturally we are going into the Wales game with confidence," O'Neill added.
"Teams are capable of taking points off each other and that's been proved."
Despite being without Daryl Murphy, Shane Duffy, Wes Hoolahan, Ciaran Clark, Harry Arter and Robbie Brady, O'Neill believes he has enough depth to cope.
"We've lost a couple of big players but we have players who can come in and who want to play. Regardless of what league they're in, they want to play as strongly as possible if they want to get in the team," he said.
"I think us qualifying for the Euros and our achievements out there at the time means the younger players want to be part of it, not just in the squad, but in the team."
Republic of Ireland will have to perform as well as they did to beat Italy at Euro 2016 when they face Wales in a World Cup qualifier on Friday, says manager Martin O'Neill.