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.
Read the full article on eurosport.co.uk: Republic boss Martin O'Neill rejects talk of Wales 'lull' after Euro 2016 run