In 2006 the WRU made all blacks do the haka in changing room and here's why
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.
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.