Koeman blamed O'Neill for giving McCarthy too much game time in two 2018 World Cup qualifiers last month
Koeman blamed O'Neill for giving McCarthy too much game time in two 2018 World Cup qualifiers last month as he had just returned from a groin operation.
O'Neill said the Dutchman's claim was rubbish even though McCarthy has only played just over an hour for Everton since the qualifiers.
Ireland beat both Georgia and Moldova to go level on points with table-topping Serbia as the Irish bid to reach their first World Cup finals since 2002.
"I totally refute that," O'Neill told a press conference after he announced a 35-man squad for the next World Cup qualifier against Austria in Vienna on Saturday week.
"James had declared himself fit. He played the first game and came off in the second not because he was injured but because he was tired.
"And, remarkably, he trained the very day their manager was bleating about it."
O'Neill, who guided the Irish to the last 16 of Euro 2016 where they lost to eventual finalists France, selected McCarthy in his squad even though the 25-year-old is hampered by a hamstring problem.
"I have included James at this minute. Speaking to him, James is improving day-by-day," said O'Neill, who also gave surprise call-ups to home-based duo Daryl Horgan and Andy Boyle who have impressed during Dundalk's European campaign.
"If the game for instance was this weekend, he wouldn't make it. The following weekend? I would say he would be doubtful at this minute. He needs to get some proper training in.
"He has been doing a little bit, but it's one of those. I'll leave him in for the provisional squad and we'll see how things go. Obviously he wouldn't make it this week and he would need to something a little bit before that."
Goalkeepers: Darren Randolph (West Ham/ENG), Keiren Westwood (Sheffield Wednesday/ENG), Colin Doyle (Bradford/ENG), Ian Lawlor (Manchester City/ENG), Danny Rogers (Falkirk/SCO)
Defenders: Seamus Coleman (Everton/ENG), Cyrus Christie, Richard Keogh, Alex Pearce (all Derby/ENG), John O'Shea (Sunderland/ENG), Ciaran Clark (Newcastle/ENG), Paul McShane (Reading/ENG), Shane Duffy (Brighton/ENG), Andy Boyle (Dundalk), Stephen Ward (Burnley/ENG)
Midfielders: Aiden McGeady (Preston/ENG), James McClean (West Brom/ENG), Jeff Hendrick (Burnley/ENG), James McCarthy (Everton/ENG), Stephen Quinn (Reading/ENG), Glenn Whelan (Stoke/ENG), Harry Arter (Bournemouth/ENG), Eunan O'Kane (Leeds/ENG), David Meyler (Hull/ENG), Stephen Gleeson (Birmingham/ENG), Conor Hourihane (Barnsley/ENG), Robbie Brady, Wes Hoolahan (both Norwich/ENG), Callum O'Dowda (Bristol City/ENG), Jonathan Hayes (Aberdeen/SCO), Daryl Horgan (Dundalk)
Forwards: Jonathan Walters (Stoke/ENG), Adam Rooney (Aberdeen/SCO), Kevin Doyle (Colorado Rapids/USA), David McGoldrick (Ipswich/ENG)