McCarthy has been ruled out of Saturday's vital Merseyside derby against Liverpool after suffering a hamstring problem while on international duty with Ireland.
Despite missing Everton's last two games because of a hamstring complaint, McCarthy was named in the Republic's starting line-up for their World Cup qualifier against Wales last Friday, only to then be forced to withdraw having aggravated it just before kick-off.
Koeman admitted the player needed to take responsibility as well, but he was especially critical of O'Neill, who had already been criticised by the Dutchman earlier this season over McCarthy's use by the Republic after suffering another injury.
"James had an injury when he reported for Ireland duty last week. Our medical team made the Ireland medical team aware of this, of course," said Koeman, who also lost star fullback Seamus Coleman while on Ireland duty due to a horrific double leg break.
"Everton's medical team advised extreme caution, not only due to the current injury but due to previous injuries too, and the assessment by the Ireland medical team was that it would be a high risk for James to play against Wales.
"But, of course, James has a strong desire to play for his country. So, when asked if he was fit to play, he said he felt he was fit, and he was selected to start the game by the Ireland manager who, in my opinion, in this instance was not protecting the player.
"Clearly James was not fit to play. He had trained only for two days with Ireland and he broke down during the warm up."
O'Neill, who guided Ireland to the knockout stages of the Euro 2016 tournament and presently they are second in their 2018 World C up qualifying group, hit back strongly later on Friday.
"Once again the Everton manager, master tactician of the blame game, has struck out in his comments today, criticising both myself and James McCarthy," said the 65-year-old Northern Irishman in a statement.
"Perhaps a review of Everton's pre-season programme might provide some enlightenment.
"James had a magnificent tournament for the Republic of Ireland last summer during UEFA EURO 2016, playing his last game in very late June.
"He then returned to Everton after a very short break, but only 11 days later, he played his first of three games, all within an eight-day period, against Real Betis, Manchester United and Espanyol. Overloading?"