Ireland paid the price for having three spot-kicks saved as they were denied a place in the quarter-finals.
But McCarthy refused to blame the players who missed and praised the way the side had battled back to force extra-time.
It's very tough for the lads who took the penalties and I've got no criticism of them at all
"I'm very proud. We didn't deserve an end like that - we deserved to win in normal time," he said.
"They are a wonderful bunch of people. I'm proud to have had a chance to work with them.
"I said to them before the penalties 'whatever happens there will be no recriminations'.
"We've had a wonderful World Cup. We would have loved to go to the quarter-final and we deserved to.
"I've nothing but admiration for the players - even the ones who didn't play.
"It's very tough for the lads who took the penalties and I've got no criticism of them at all."