Hunt was not impressed with the way the Republic of Ireland conceded the second goal of the match in the 3-0 defeat to Belgium on Saturday.
Full-back Thomas Meunier swung in a cross into the Republic of Ireland penalty box, and midfielder Axel Witsel headed home from close range.
Hunt claimed on Twitter that Everton midfielder McCarthy was caught ball-watching. The 33-year-old Republic of Ireland international striker, who is not part of Martin O’Neill’s squad for the Euro 2016 finals in France, posted the following message on the social networking site immediately after Belgium scored their goal of the Group E game on Saturday:
Aww that's killed is!! McCarthy cought ball watching in the last seconds!!! We'll keep fighting tho!! #COYBIG— Noel Hunt (@boyhunt) June 18, 2016
Former Everton and Republic of Ireland international star Kevin Kilbane also criticised McCarthy for his role in Witsel’s goal.
"It's far too easy,” said Kilbane on BBC Sport (15:20, June 18). “Axel Witsel drifts in from the edge of the penalty area for a free header.
"Nobody tracks the run. He just runs off the back of James McCarthy - he's got to track the run or take a shout from behind to leave him.”
Everton striker Romelu Lukaku was the star of the show in the Euro 2016 Group E match at Nouveau Stade de Bordeaux in Bordeaux.
The former Chelsea striker scored twice for the Belgians, who bounced back perfectly from the 2-0 defeat to Italy in their opening game at the tournament with a comfortable 3-0 victory.