"We're obviously very disappointed. To concede six goals you can't be happy so we're not today," lamented Milne, who got his marching orders a minute before regulation fulltime after yanking the shirt of substitute striker Raymond Gunemba in the 86th and then reeling in the PNG international around the shoulder in the 89th.
Wanderers drew first blood in the 18th minute from striker Godwin Darkwa after he pounced on rightback Martin Canales Ramos' blind pass to Milne to put the hosts up 1-0.
Bay striker Saul Halpin levelled terms, 1-1, when Fergus Neil put a pass out wide to striker Angus Kilkolly, who deftly gave the scorer a tap-in goal in the 38th minute.
But the silly argy-bargy stuff resulted in Sean Liddicoat picking up his first yellow card for ankle tapping Roussin Nkoy in the 41st minute, although referee Cory Mills and his assistants failed to comprehend that the Bay defender was retaliating to Nkoy grabbing his shirt seconds before in the tussle.
Liddicoat's sending off came in the 18m box for pulling down Jack Salter from behind in the 49th minute as Bailey Webster stepped up to adroitly slot the penalty kick, 2-1, past keeper Joshua Hill.
The ugliness cropped up again in the 53rd minute when Milne and Hamilton keeper Matt Oliver clashed midair in a cornerkick collision but the Bay skipper made the mistake of walking off the pitch for medical attention so when play resumed he found himself on the sideline.
Oliver hoofed the ball up the park, Darkwa brought it down before pushing it to striker Marc Evans, who beat Nile Walwyn to score for a 3-1 lead.
Stung into action, Bay striker Sam Mason-Smith narrowed the lead, 3-2, with a pearler drive to the roof of the net from a free kick the Wanderers' wall had failed to mop up in the 65th minute.
Four minutes later Ross Willox repaid Angell's faith as a substitute when he threaded a ball to Mason-Smith to smash into the net in similar fashion to equalise, 3-all.
Gunemba then terrorised the Bay, threatening before making it 4-3 at the inside post with a dead-foot cradle on the volley from the left-flank cross.
He became provider in the 76th minute from a left-footed cornerkick that keeper Hill fumbled, enabling centreback Sam Redwood to knock the ball in with his thigh, 5-3.
A minute into added time Salter rubbed the proverbial into the wound against nine men with Halpin helping it in, 6-3, before Bay substitute striker Ben Everson dispossessed Redwood 20m out before making it 6-4 for his maiden goal for the franchise in his debut season.
So how did all the histrionics creep into the game?
"They had their backs up against the wall and they needed the win with some bad performances and we were fighting to keep our run going," said Milne.
"Perhaps we didn't deal their style of play within our structures well enough."
Milne didn't think the Wanderers were that well structured in their play but were quite direct, leaving them floundering in dealing with long balls and fleet-footed players who made life hectic.
"In saying that we were down to 10 men and we still came back to level 3-all but then things fell apart again so that's disappointing."
The game didn't have a fairy-tale finish like Bay United had had against Wellington Phoenix Reserves in the 5-all affair at Park Island, Napier, last summer.
The Bay now have time to dwell on their shortcomings while training between festivities for their next outing on Sunday, January 8, away at the Trusts Arena against Waitakere United.
"We can still finish in the top four to give ourselves a good chance to go on to winning [the title] because we're so close this season so there's no question about that."
Milne expects the game to be fuelled with emotions after Waitakere had lodged a "please confirm" to the premiership arm of the NZ Football on Bay United's composition after the first-round loss in Napier.
The Bay franchise was cleared of assertions that the team had fielded more than the allocated number of foreigners in it's playing squad.
"They might play quite similar to the way Hamilton played today, I don't know but we'll work that out in the new year," Milne said.