McCaw was speaking after being “blown away” by a huge crowd turn-out, estimated at more than 150,000, for a parade through the central city on Monday.
The All Blacks’ narrowest of victories over the Tricolores, by 8-7, gave them the Webb Ellis Cup for only the second time and after a gap of 24 years.
“No, not really,” McCaw said, when asked if the feat had registered fully with him yet.
“The first time I felt it was just coming up [Queen St]. Like I said last night, it was relief that we got through.
“Everyone absolutely had nothing left. It was sort of a funny feeling, really. It will sink in, I’m sure.”
The parade is the first of three in the country over consecutive days, the others being in earthquake-ravaged Christchurch and in Wellington.
McCaw said the numbers that came out in Auckland topped off the backing the team had received from fans during the entire tournament.
“I was blown away, really,” he said.
“It showed the amount of support and passion there is for the All Blacks and for rugby in New Zealand.”
He said it wasn’t something the All Blacks had underestimated.
“But to see people come out and show their support and is pretty awesome, because Kiwis sometimes don’t show emotion too much, and there was plenty of that there.”
The World Cup was the one major trophy that had been missing from the 30-year-old flanker’s remarkable CV, which includes 103 Tests, 66 of them as captain – both New Zealand records.
What makes McCaw’s leadership even more impressive over the past seven weeks is that he has been battling with a niggling foot injury for most of this year.
The problem restricted the amount of training he could do with the team during the tournament and also forced him to be a late scratching from one of the pool matches.
“I’ll obviously get it looked at in the next couple of weeks,” he said about the additional treatment he would need.
“What it will be, we’ll find out. To be honest, I’m not too worried about it at the moment.”