Carter, who has amassed a record 1250 points during his 85-cap Test career, had been due to captain the All Blacks in their final Pool A fixture against Canada while regular skipper Richie McCaw rested a foot injury.
But the 29-year-old tore a groin tendon in kicking practice during Saturday's eve-of-match training session, ending his participation in the tournament.
"I encourage everyone to move on - I have," said Carter, who has been replaced in the squad by Manawatu back Aaron Cruden.
"I'm pretty disappointed, but I'm now here to help the team and I think everyone should move on too."
Colin Slade replaced Carter in the team against Canada and head coach Graham Henry has backed the replacement to step up.
Carter also believes the All Blacks can cope with his absence, beginning with the quarter-final against Argentina on Sunday in Auckland.
Carter added: "The team are pretty focused. If we lose any player we've got enough depth and we've got such a good squad that players come in and fill their roles.
"We're in the play-off stages; we've got effectively a final this week. Anything can happen.
"We just have to go out there and put everything on the line like there's no tomorrow."
Carter suffered the injury during a kicking drill at Rugby League Park in Wellington.
"I knew it was pretty serious because of the pain," he said.
"I thought it was quite unusual; I've kicked thousands of balls.
"It felt like it popped, hence going down to the ground in agony.
"It's quite hard to explain. I was just going through my usual routine.
"I was actually having a bit of a shorter session than usual.
"I normally kick a good 15, 20 balls at captain's run, but I was only having four this time around.
"It was my fourth kick and I didn't know what happened.
"It's just really unfortunate."
Carter insisted there was no pre-condition which led to the blow.
He added: "It's really frustrating. The pure randomness of the injury and for it to come out of the blue.
"My body was really good going into the week and I haven't had any groin or adductor or hip problems in the past.
"For something like this to happen has been really tough. I can't put my finger on why. I'm constantly asking 'why did this happen?'
"I don't have the answer unfortunately."
The Crusaders fly-half now says he has come to terms with the blow, but experienced an emotional roller-coaster.
"It was a pretty tough night (on Saturday) knowing my World Cup was over," he added.
"Being around the team spurs me on to think positively and help them out in whatever way. Moping about is not going to help them.
"It's a little bit different behind closed doors; I tend to let out my frustration a lot.
"Lying in bed on Saturday night was pretty tough, looking back at one of the craziest days of my life.
"To be named All Black captain - something very special - and to have that taken away from you through an injury and then later to find out that my dream of being involved in the World Cup was now over.
"It's pretty gut-wrenching and disappointing what happened, but I have to get over that and continue to think positively and try and help the guys in whatever way I can."
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