Mackay was dismissed following months of unrest at the Cardiff City Stadium, despite securing promotion to the Premier League last term, with owner Tan criticising the Scot's pre-season transfer activity and subsequent style of play.
Iain Moody was sacked from his post as head of recruitment and Mackay met the same fate following a 3-0 defeat at home to Southampton on Boxing Day.
The club's fans have been vociferous in their support of Mackay - and lambasting of Tan - in recent games, but it was not enough to save the 41-year-old's job.
Tan responded to the decision by blaming Mackay for the furore surrounding the club, but Cardiff's fans have now blasted the Malaysian and demanded a return to Cardiff's traditional home colours of blue as recompense for their disenchantment.
"Recent off-field controversies have damaged the relationship between the club and fans," the statement read.
"One way Mr Tan could build bridges with supporters would be to return the playing kit to blue at the earliest opportunity.
"This whole episode highlights once again the need for strong supporter engagement in football clubs at all levels.
"Our friends in the Swansea City Supporters' Trust have an excellent working relationship with the senior management of their club and a supporter director sits on the board.
"We'd like to see Cardiff City move towards that in the future."
On Mackay's own legacy at the club, the statement added: "We'd like to thank Malky sincerely for his massive contribution to Cardiff City.
"He will always be fondly remembered by Bluebirds fans as the manager who took Cardiff City to the Premier League for the first time.
"He is undoubtedly one of the best and most popular managers in Cardiff City's history."
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