Referee Beeby sent off Southampton striker Kenwyne Jones for shoving Palace defender Mark Hudson in the chest in the 28th minute.
Burley had no complaints about that decision but was fuming the Northamptonshire official let off Eagles keeper Scott Flinders with only a yellow card for handling outside his area four minutes later.
Jones saw red after becoming embroiled in a 20-man brawl on the edge of the Palace 18-yard box.
Flinders was lucky not to join the Trinidadian for an early bath when he came racing out of his box to challenge Southampton winger Rudi Skacel and kicked the ball on to his left arm.
Once the dust had settled it was left to Southampton defender Chris Baird to continue the pantomime theme by turning from hero to villain in the space of seven second-half minutes.
Baird put Southampton in front with a wonderful glancing header from a Jermaine Wright corner two minutes after the restart.
The Northern Ireland international then gifted Palace a quick-fire equaliser.
Baird was caught in possession 20 yards from goal by Palace winger Jobi McAnuff, who gleefully guided the ball past Southampton goalkeeper Kelvin Davis and into the bottom right-hand corner.
Flinders, in for the injured Julian Speroni, added to Burley's fury by pulling off a number of good saves.
Southampton midfielder Andrew Surman thought he had scored his first of the season with a right-foot curler which was heading for the top right-hand corner before Flinders came flying across his goal to pull off a superb save.
Man of the moment Flinders also tipped Gareth Bale's 25-yard free-kick on to his crossbar soon after escaping a red card.
Burley also watched Hudson produce a heroic goal-line clearance to keep out Baird's first-half header as Saints dominated the match.
Poland international and top-scorer Grzegorz Rasiak almost won it at the death when he volleyed on to the roof of the net after Bale's long shot had deflected into his path.