The Welsh Rugby Union has refused to apologise over a row that saw New Zealand performing their haka in the Millennium Stadium changing rooms.
The haka - a ceremonial war dance - is traditionally performed by New Zealand directly before kick off in matches.
But it was held in private on Saturday in protest at Wales' plan to "respond" with their own national anthem.
WRU group chief executive Roger Lewis said the issue should have been sorted out long before the match.
The haka is believed to have been performed on the field before matches by teams representing New Zealand since the 1880s.
The first game between Wales and New Zealand in 1905 saw the haka followed by the Welsh crowd singing their national anthem, Hen Wlad fy Nhadau.
This was repeated last year in a game to celebrate the centenary of tests between the two countries.
But Wales' wish to follow the haka with their anthem before Saturday's match saw New Zealand refuse to stage the haka on the field.
When asked if he would apologise, group chief executive Roger Lewis said: "I don't think anyone comes out well in this - both sides regret what happened on Saturday."
Mr Lewis told the BBC the WRU had informed their New Zealand counterparts of their plans to respond to the haka several weeks ago.
He said: "The match protocol outlining the order of events had been set by the Welsh Rugby Union to the New Zealand Rugby Union on 16 October.
New Zealand have staged the haka for more than 100 years
"However, the WRU were only officially informed by New Zealand on the morning of the match that the haka was not going to be performed.
"This kind of brinkmanship is not good for rugby, it's not fair on the fans."
Mr Lewis added that the WRU would write to world rugby's governing body, the IRB, to "suggest that a worldwide protocol for the haka is agreed to by all".
Former Wales captain Paul Thorburn told BBC Wales he believed the WRU decision had set a precedent for next year's World Cup and that other teams will also insist on their national anthems being played after the haka as a response.
He said if the All Blacks maintain their stance it could result in the haka never being performed in public again.
Professor Piri Sciascia, pro vice-chancellor Maori at Victoria University in Wellington, New Zealand, was consulted by the WRU over appropriate responses to the haka.
He said: "I don't recall a discussion that discussed the protocol of putting the haka between the national anthems.
"I was as surprised as anyone else on Sunday morning our time to see the haka not being performed.
"What I envisaged at the time is the kind of traditional Welsh singing of the national anthem or some national song in response after the haka, but something quite separate from the two formal national anthems where people stand to attention."
He added: "The advice that I was being asked about was around the validity as to whether or not the Welsh national anthem was a valid response.
"I said yes it was valid to respond and in fact whatever the way in which the Welsh people responded to the haka - that's up to them."
All Blacks captain Richie McCaw accused the WRU of trying to "mess around" with the traditions of the haka.
He said: "The tradition needs to be honoured properly if we're going to do it. If the other team wants to mess around, we'll just do the haka in the shed [changing room]."
All Blacks head coach Graham Henry said he believed it had been agreed that 2005's match, which saw the haka followed by the Welsh anthem, was a one-off.
He said: "We agreed to the change last year but we had a guarantee it wouldn't happen again. But they (the WRU) asked us to do the same this year and we said no."