Cardiff City midfielder Arter, like fellow Londoner Declan Rice of West Ham, is unavailable for Ireland due to off-field reasons, in his case primarily down to a row with assistant coach Keane back in May.
"I think you have to try to get the best players on the pitch," said McCarthy, who managed his country between 1996 and 2002.
"Everybody is going to scream 'hold on, what about the 2002 World Cup when you sent Roy Keane home?' However, I did invite him back - the offer was there. That was me knowing that it was almost like the weight of the people that wanted him back. I had to offer that olive branch.
"I don't want to bring that case up again because it was all dragged out during the summer when the World Cup came around. Blah, blah, blah, it was bull***t.
"But I'm talking about having the best players on the pitch for Ireland and I don't know what Harry's argument was about."