Delaney, 34, was a notable absentee from O'Neill's provisional 40-man panel for the upcoming Euro 2016 warm-up friendlies against Switzerland and Slovakia and the Ireland boss indicated that he would rather look to the future with defenders such as Blackburn Rovers' Shane Duffy.
"I’ve got six centre-halves! There’s people here that have done brilliantly for me and helped us qualify, and I’ve got one or two younger lads coming through like Shane Duffy, who I feel has international football ahead of him," O'Neill said.
"I don’t know how much more you want me to say, Damien’s 35 [sic] and Shane isn’t."
Reacting to the news of Delaney's exclusion, former Ireland international Dunphy said that "it's not right that the Irish team should be deprived of a player because of personal differences."
"It’s wrong. This guy is playing in the Premier League, he’s a very good player. He’s been in the Premier League all year," Dunphy told RTE's 'Game On' programme.
"We have Paul McShane, who’s playing for Reading and he’s not a very good defender. The guy at Derby County (Richard Keogh), not a very good defender and has had a couple of nightmares. And, we’ve got a Premier League player and we’re not even putting him on the plane?
"That’s not right for the fans, the other players; this guy should be in the team really, and he certainly should be in the squad."
Delaney previously featured for Ireland under O'Neill in the summer of 2014, playing a friendly game against Turkey in Dublin. However, according to the former Celtic boss, the defender was not willing to travel to the United States for subsequent friendlies against Portugal and Costa Rica.
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While not ruling out a potential return for the Cork native, O'Neill admitted that such a refusal "didn't augur too well."
"I think Damien felt that he was never going to be a first choice at the time and declined to go to America," the Derry native said in February. "I mean that didn’t augur too well, whatever he says about it, he said that he would make himself available if he had a decent chance of getting into the squad, or into the team.
"I wasn’t in the position to actually make those decisions. I couldn’t guarantee anybody in the side. So we went our separate ways at that time."
Dunphy believes that "personal differences" should not be a reason to excluded Delaney and pointed to the lack of Irish defenders plying their trade in the Premier League.
"It’s not right that the Irish team should be deprived of a player because of personal differences," added the Dublin native.
"It should not be happening. This guy is top class. We don’t have any Premier League defenders apart from John O’Shea- the other guy is injured, from Stoke (Marc Wilson) So, something is not right there."