"So yeah, without a shadow of a doubt I want him here. The team wants him here. We play better football under him. And if we let him go, I think it's absolutely detrimental to New Zealand football."
For his part, Hay said he wants to continue, but would require assurances about a commitment to more games, against better quality opposition and regular fixtures in New Zealand. He confirmed there hasn't been any dialogue over his future.
"I haven't had any communication from anybody from New Zealand football for quite some time now," said Hay. "So ultimately, the ball's in their court and we'll just leave it there until they make contact."
When the coach was asked if he would initiate contact, Wood interjected quickly:
"I don't think he should," said Wood. "They should be coming to him because he has broadcast his talents. He's shown what he can do with this team. They should be coming to him."
Hay's frustration was probably exacerbated by Sunday's performance, which he labelled as one of the worst of his tenure, though Socceroos' coach Graham Arnold admitted fatigue was a major factor, as he had the luxury of using an entirely new team, while most of the All Whites backed up from Thursday's game in Brisbane.
New Zealand also suffered hugely from losing Wood to a first-half rib injury.
"I couldn't breathe properly," said Wood. "I couldn't really run. I'm extremely gutted that I've had to come off, especially in the home game."
Wood and Hay also paid tribute to retiring captain Winston Reid, who got an emotional – if not fairytale – farewell.