The Everton man struggled on international duty this evening.
The Spanish manager was dismissed from his role with the Toffees in May as Everton endured a second successive 11th-placed finish in the Premier League which, given their squad, is gross underachievement.
McCarthy, who played 29 Premier League games this past season, was back in action tonight as the Republic of Ireland were held to a 1-1 draw by Sweden.
The 25-year-old midfielder looked to struggle at times and gave the referee a big decision to make in the second half following a rash challenge having already been booked, though he was spared.
The outspoken Dunphy was blunt in his assessment of the Scotland-born midfielder, whom he claims got Martinez fired from the Merseyside club.
"McCarthy we have to do something about," he told RTE Sport. "I watched him all season at Everton and he got his manager sacked over there.
"The guy does nothing [except] stroll around the pitch like a traffic cop pointing around."
It is probable that Dunphy is referring to a lack of effort on McCarthy's part when he claims he is responsible for Martinez's dismissal, though nobody, with perhaps the exception of 25-goal striker Romelu Lukaku, really covered themselves in glory on the blue half of Merseyside in the 2015-16 campaign.