Former Republic boss McCarthy grinned and remained silent when asked how new coach Martin O'Neill and his assistant Roy Keane might fare after being confirmed in their new roles this week.
McCarthy memorably fell out with Keane on the eve of the 2002 World Cup finals, prompting the former Manchester United midfielder to leave his squad before the tournament.
A decade on and Keane now finds himself in a similar role to McCarthy, but the 54-year-old was determined not to rake over old ground.
Asked how he thought O'Neill and Keane would get on, an apparently amused McCarthy remained silent for consecutive questions before eventually replying to a journalist: "I'm just a little bit confused about you actually."
McCarthy, now in charge of Sky Bet Championship side Ipswich, was more forthcoming when asked about his own time in charge of the Republic.
The Barnsley-born boss, who had ruled himself out of a return to the Republic before O'Neill got the job, guided them to the round-of-16 in Japan and South Korea in Keane's absence.
"I was in the hot seat and I loved it," he said in the press conference shown on Sky Sports News.
"I had a great time. We went from 59th to 13th in the world, I think, and lost in the last 16 of the World Cup in 2002 on penalties.
"I had a great time. I loved it. I was quite successful actually."
When then asked how he thought Irish fans would take to the new coaching set-up, McCarthy responded only with laughter.