Bev Carter, who spoke to The New Zealand Herald at her Southbridge home, said her husband Neville had taken the news hard.
They did not feel up to speaking publicly about their son's injury.
Mr Carter later told TVNZ that he had been unable to sleep on Saturday evening because he was busy consoling his wife and son.
"[Daniel's] pretty upset, of course, and he would be, because of all the hard work he has put into it," he said.
The bad news did not stop Mr Carter joining his fellow Southbridge Volunteer Fire Brigade firefighters to put out a hedge fire in his home town yesterday.
Mr Carter told fellow volunteers "these things happen".
"You've just got to get on with it. It's just one of those things in life."
The Southbridge community took the news hard. Local rugby club captain Gary McGregor said Carter's injury had "hit us like another earthquake".
Club manager Chris McMillan, who knows the Carter family well, said his heart dropped when he heard the news.
"Just really gutted for Dan himself because I know how much it meant to him - especially this World Cup being played in New Zealand," he said.
"Injuries happen, so you've just got to make the best out of a bad situation, I suppose."
Southbridge hotelier Russell Guenole said locals began arriving at the pub about 4.30pm on Saturday with the news Carter was out of the cup.
"A lot of them were just gutted - especially those that know [Carter]."
• Telegraph rugby writer Paul Ackford was sympathetic, saying the tournament would be less of spectacle without Carter: "He is 29 and unlikely to make the next World Cup. This was his stage, his country, his tournament, the crowning glory of a majestic career. And now he is dust."
Carter's Australian opposite Quade Cooper also empathised with the All Black's early exit.
"As much of a war the World Cup is, you never like to see players missing out on a tournament you work so hard to get to."
Former England hooker Brian Moore summed up the collective sigh of relief from opposing countries when he commented on Twitter: "Dan Carter out for whole tournament ... things suddenly go better for everyone else - ever seen a whole country wobble?"
