Seeing Andy Linighan equalise for Arsenal in the overtime Mike Riley allowed was all too much for them. "He (the referee) destroyed a beautiful game," Curcic said. Not the game, but a victory that would have put Villa on top of the Premiership.
Sometimes you have to wonder what goes on in the minds of footballers. They can count their cash, of course, but not, it seems, weigh up the cost of pointless protests. It is easy enough to get booked these days without looking for trouble, which is what Curcic and Staunton did when it was finally over.
Probably, the Villa manager, Brian Little, had words with them about this, especially as he was rather more philosophical. "The amount of time added on did seem a lot," Little said, "but perhaps at some stage in the season it will work in our favour."
Last week it worked against Arsenal when Dennis Wise equalised for Chelsea in overtime. "You just have to accept that it isn't over until it's over," Arsenal's caretaker manager, Stewart Houston, said. In other words, no longer 45 minutes each way but exactly as the referee calls it.
In any case, Villa had only themselves to blame for getting all wound up when Arsenal gambled on throwing more men forward.
"We panicked a bit," Little said. That is putting it mildly. When Arsenal abandoned a system designed for what managers like to call "keeping a clean sheet", bringing on John Hartson for the defender Steve Morrow, all the composure went out of Villa's defence. It did not help when they began to give the ball away and lost the knack of holding it up in Arsenal's half.
Villa had been coasting with the advantage of Savo Milosevic's two goals, but they were thrown out of gear by Arsenal's spirited comeback.
Nobody did more to unsettle them than Paul Merson, who caused no end of trouble when released to run with the ball. If Merson's troubles are now all behind him, on this form he could come back into the England reckoning. With Merson spearheading a revival - "after conceding two disappointing goals, it was a case of 'Here we go again'," Houston said - it became an exciting match that emphasised the extent of Arsenal's character.
Things, suddenly, were going every which way. In the 70th minute Dennis Bergkamp broke left and picked out Merson with a cross that Merson headed past Michael Oakes, who is performing well as a deputy for the injured Mark Bosnich.
Until then there had been plenty to admire in Villa's enterprising football, particularly the ease with which they switch positions and responsibility.
Granted the initiative by Arsenal, they survived a scare when Merson's nudge against the crossbar rebounded on to the goal-line. In this instance, certainly, the referee was spot on with his judgement, television replays showing that the ball had not crossed the line.
The protest that Milosevic had strayed offside before wrong-footing John Lukic to put Villa ahead in the 39th minute was, as television suggested, probably more legitimate.
Either way, it will be interesting to see what the Football Association come up with in an attempt to eradicate these thorny issues.
Milosevic's second was down to bad defending. Dwight Yorke was given room in which to sting Lukic's fingers, and the ball fell invitingly for the Yugoslav.
Doubtless, Linighan's equaliser will lead to some words about lack of concentration. Villa were aware that Arsenal are dangerous at corner kicks but they could not prevent Martin Keown from flicking on Merson's inswinger.
"That was a lesson out there today," Little added, "and I hope the players learned from it." One thing Curcic and Staunton should have learned is the value of keeping your mouth shut.
Goals: Milosevic (39) 1-0, (63) 2-0; Merson (70) 2-1; Linighan (90) 2-2.
Aston Villa (3-4-1-2): Oakes; Curcic, Staunton, Southgate; Wright, Ehiogu, Townsend, Nelson (Taylor, 60); Draper; Yorke, Milosevic (Johnson, 84). Substitutes not used: McGrath, Scimeca, Rachel (gk).
Arsenal (5-3-2) Lukic: Dixon, Winterburn, Linighan, Keown, Parlour; Platt, Wright, Merson; Bergkamp (Helder, 80), Morrow (Hartson, 67). Substitutes not used: Shaw, Rose, Harper (gk).
Referee: M Riley (Leeds).
Bookings: Aston Villa: Curcic, Staunton. Arsenal: Platt, Wright, Morrow, Hartson.
Man of the match: Merson.