Chris Coleman's men upset the odds in France last summer to make it all the way to the semi-finals, where they only succumbed to eventual winners Portugal.
However, while they remain unbeaten in their World Cup qualifying campaign, which rolls into Dublin on Friday evening, they have drawn three of their opening four fixtures and find themselves four points adrift of Group D leaders Ireland.
Failure to win at the Aviva Stadium would leave Wales with a great deal of work to do in the second half of the campaign, but O'Neill insists they remain as dangerous as ever.
He said: "Expectation is very, very high, not only in Wales itself. The expectation from within Europe itself is that Wales are very, very capable. They possess some excellent players in their side and obviously a world-class player in Gareth Bale.
"No, I don't think there's been any lull. Perhaps they might have thought they'd have won one of those matches.
"But the Georgia game, which they could easily have been beaten in, that was never going to easy at all. We had played them (Georgia) a few days earlier and Seamus (Coleman) got the goal to win the game, but they played brilliantly in the first half against us in the match, so the games are not easy.
"But are Wales suffering? I don't see that at all, I genuinely don't see that. Wales are capable of winning football matches home or away."
There is little danger of anyone within the Republic camp underestimating Wales, particularly with O'Neill's squad having been ravaged by injury and suspension.
That is due in part to the intensity provided by the manager, and perhaps even more so by his assistant Roy Keane, the former Republic and Manchester United midfielder.
Captain Coleman said: "It's great having Roy around. He knows what it means to put on the green shirt.
"Between Roy and the manager, the first thing that comes to mind is that they're winners, so it's ideal for us players to look up to.
"If things are getting a bit sloppy around the place, we'll be told."
Coleman and Everton team-mate Ashley Williams will lead their respective teams into battle, but there will be no pleasantries until after the final whistle.
The Irishman said: "I've got to know Ashley quite well at club level. He's a great lad, but he's a winner as well. But once I've got that green shirt on, that's all I care about."
