The 73-year-old argued that the current squad does not possess the same strength as when the former Manchester United man used to play for the Boys in Green
As a television pundit for ITV during Ireland's 4-0 demolition by European champions Spain, Keane criticised the side's display and the idea that supporters are not bothered if their country lose.
The Italian reacted angrily to the former Sunderland and Ipswich manager's comments, acknowledging that Keane was a great player but that Ireland's squad was a lot stronger back then.
"Roy Keane was a very good player," the 73-year-old told reporters. "We know Ireland, when we played against him, was a strong team. This generation was very hard. It is not my habit to be critical of other colleagues as coaches or managers, but what has he done after he finished playing?
"The players were strong in his time, playing at Manchester United, playing at Celtic, playing everywhere. They were a strong team.
"Roy Keane was a great player. He obtained very good results as a player. Now that he is a coach he should just stick to focusing on getting results as a coach."
The former central-midfielder, who is not new to controversy with the national side following his row with Mick McCarthy during the World Cup in 2002, was not happy at perceptions about Irish fans and also thought the team should have done better at the tournament.
During broadcast on ITV the 40-year-old said: "It's a reality check for a lot of the Irish players. I think a lot of them think they are top players, and it goes to show that they are so far behind a lot of these players.
"I think the players and even the supporters, they all have to change their mentality. It's just nonsense from players speaking after the games about how great the supporters are.
"Listen, the supporters want to see the team doing a lot better and not giving daft goals away like that. I'm not too happy with all that nonsense.
"To praise the supporters for sake of it, let's change that attitude towards Irish supporters. They want to see the team winning - let's not kid ourselves, we are a small country, we are up against it, but let's not just go along for the sing-song every now and again."