Mackay watched his side lose 3-0 at home to a Southampton side who claimed a first win in seven games thanks to a double from Jay Rodriguez and a Rickie Lambert strike.
The on-field performance added to the sense of off-field discontent caused by the ongoing battle between Mackay and Tan which has put the manager's position in jeopardy.
The lingering uncertainty over Mackay's future, despite a statement from chairman Mehmet Dalman that he would be in charge for the "foreseeable future", fuelled a pre-match protest where a group of supporters voiced their disapproval of Tan's running of the club. Chants of 'Don't sack Malky Mackay' and 'We'll always be blue' also rang around the stadium during the game.
Mackay revealed earlier this week that Tan had rejected two requests for the duo and Dalman to meet in an attempt to reconcile their differences. Asked if a date had been set, Mackay said: "Not as far as I'm aware. I've not been told of any meeting. I don't usually talk to him [Tan] on a game day. That's not something that normally happens. I usually speak to other people. I was informed we would try to have a meeting."
Theo Walcott's second double in 12 days took Arsenal back to the top of the table as Arsene Wenger's men came from behind to beat West Ham 3-1 at Upton Park. The hosts stole a 1-0 second-half lead through Carlton Cole but Walcott scored twice in three minutes to take his season's goal tally to five while Lukas Podolski also marked his return with a goal.
Goal-shy Chelsea were unconvincing as they secured second place with a 1-0 home victory over Swansea thanks to Eden Hazard's first-half goal.
Manchester United showed the conviction of old as they they came from 2-0 down after 13 minutes to beat Hull City 3-2. Defender James Chester and David Meyler put Steve Bruce's side ahead at the KC Stadium but if the manager started to sniff a first victory over his old club, any such thoughts vanished thanks to quickfire goals from Chris Smalling and Wayne Rooney.
Rooney's 150th Premier League goal for United levelled the game before the half-hour mark and the scores stayed locked until midway through the second half, when Chester put through his own net under pressure from Rooney.
Everton's hopes of completing 2013 without a league defeat at Goodison Park were ended after goalkeeper Tim Howard's red card gifted bottom club Sunderland a 1-0 victory. The American struggled to deal with Leon Osman's undersold back-pass, and they paid the price when he tripped Ki Sung-Yueng, who then scoring from the penalty spot.
Loic Remy scored twice for Newcastle United in a 5-1 home win over Stoke City who had taken the lead but were reduced to nine men before halftime with Glenn Whelan and Marc Wilson both sent off. Stoke manager Mark Hughes was also dismissed.
Tottenham Hotspur lost ground as they were held 1-1 at home by West Bromwich Albion in Tim Sherwood's first game in charge since being named as the permanent replacement for Andre Villas-Boas.
Crystal Palace moved out of the relegation zone at West Ham's expense thanks to a 1-0 win at Aston Villa while Fulham were 2-1 winners at Norwich City, who had led through a Gary Hooper goal, his seventh league goal since joining from Celtic and fourth in successive home games.