O'Neill described Koeman's concerns as "nonsense" on Wednesday, adding the Everton boss should be "embarrassed" by his "bleating".
Koeman said on Thursday that McCarthy was not fit enough to warrant inclusion in Ireland's latest squad.
"The player is not fit. The player is not involved in team sessions," he told a news conference ahead of Everton's trip to fourth-placed Chelsea in the Premier League on Saturday.
"I think to have a call-up he needs to be close to being fit but it's a little bit the same story to what happened last time.
"My advice to James is stay here and do training and be fit as soon as possible but the final decision is for the player."
Koeman said he would not be speaking to O'Neill about the issue.
"No, it's not necessary because we have contact between the medical staff," he added. "And if the managers don't take the right decision, maybe he can take the good advice of the medical staff.
"I talk about him and he's talking about me and let's stop. That's the best."
Everton are sixth in the table and Koeman spoke about how he had worked to improve defensively on the training ground.
"They conceded 14 goals from set plays last season and that's crazy," said the former Southampton manager.
"We are giving more attention to set plays at least twice a week. This morning we had a meeting about Chelsea but only about set plays."
(Reporting by Simon Jennings in Bengaluru; Editing by Tony Jimenez)
Share
