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The All Whites were expected at the event organised by expat organisation Kea the morning after their 1-1 draw with China, but only New Zealand Football (NZF) chairman Fran van Hattum showed.
Kiwi dairy businessman Howard Moore said on Facebook it was a bad look, especially after a number of the team went to the exclusive M1nt Club - which has its own shark tank and ranks third in global venue sales of Dom Perignon - after the match.
"Great to see the All Whites vs China last night here in Shanghai," Moore wrote.
"The All Whites probably deserved to win based on their second half performance but it probably didn't really matter. But the All Whites' efforts were obliterated by their failure to turn up the next morning at a KEA breakfast function to which many kids came along expecting to see the All Whites as advertised.
"The reality was they went out to the M1nt Bar nightclub and couldn't make the effort to turn up for this breakfast. The All Whites were paid by MFAT to play in this game and, as ambassadors for New Zealand, should have been able to muster some of their team to turn up.
"New Zealand Soccer is never going to win the hearts and minds of the New Zealand population if this is the attitude they are going to take. Everyone of course is making comparisons with the All Blacks. They would have turned up with some of their number."
Mr Moore's wife Gillian said "poor wee kids" were left waiting with pen and paper - including one family who had travelled from Hong Kong.
Mr McKavanagh said they were unaware of the function until after the game but should have made more effort to arrange for some players to show.
"We unreservedly apologise to those who expected to see us there and were disappointed," he said. "The first I knew about it was after the game and it wasn't on the team schedule for the tour. I am just trying to track down what was going on.
"We were still trying to find out details when we got back to the hotel but everyone tends to disperse then. In hindsight, we could have got more done around it and are really disappointed that it didn't occur. It's one of those things we have to pick up and understand how the event got organised without us having a clear understanding of it and make sure it doesn't happen again."
The episode could lead to some diplomatic fallout because the game was organised with the help of the New Zealand and Chinese governments. There were also hopes beforehand the two nations would play more regularly.
Mr McKavanagh said they plan to arrange for striker Chris Killen, who plays club football in China, to be a guest at a future breakfast and hand out some memorabilia.
"When we get the opportunity at one of their functions, we will get Chris along to meet with them."