He added he did not know what decision to expect from Tan, with whom he last spoke face-to-face "a while ago".
Tan flew into London on Friday after being convinced by Bluebirds chairman Mehmet Dalman to hold one final round of talks.
A source close to the negotiations said they were "productive", but there was no resolution one way or the other.
Mackay's Cardiff farewell?
The Cardiff owner had previously given Dalman the go-ahead to begin the process of appointing Mackay's successor and was deciding whether to sack the Scot before or after the Liverpool game.
Cardiff striker Craig Bellamy was asked by chief executive Simon Lim late last week if he would take charge of the team on an interim basis but said no, and told Mackay about the approach.
Mackay said he could not "look himself in the mirror" if he were to quit.
BBC Radio Wales
why he will not resign, he said: "Because I've got a steely determination and a passion for my job and for what I do and have done for the football club for the last two-and-a-half years.
"The basis of my job, along with a lot of other things, is to prepare a team on a Saturday at three o'clock to go out and play in the best league in the world - and we are making a good job of that overall.
"Anything after that is out of my control and something that you should be finding out from other people at our football club."
He stayed on the pitch after Saturday's match to applaud Cardiff's fans, who had chanted support for the Scot and held up banners against Tan.
Before kick-off, Mackay was asked whether he had received an ultimatum from the owner about his future.
Tan's controversies at Cardiff
Changed the shirt colours from blue to red and added a red dragon to the club's crest
Removed head of recruitment Iain Moody, and hired 23-year-old Alisher Apsalyamov, who was on work experience at the club and is a friend of his son
Tried to influence the tactics of the first team during matches, reports BBC Radio 5 live's Pat Murphy
"These are things I will deal with in time," said the former Watford boss.
Dalman has a preferred candidate to replace Mackay - the manager is a high-profile name working outside the UK.
It is understood he would be keen to join Cardiff, but only if given binding assurances about his working relationship with Tan.
Tan did speak to former Bluebirds boss Dave Jones about a return to the club in some capacity, but he does not intend to follow through with that idea. Jones was
replaced by Mackay in June 2011.
The owner sent Mackay a letter by email on Monday listing his grievances at length. Their relationship is understood to be beyond repair.
Assistant manager David Kerslake, rather than Mackay,
faced the media on Friday
ahead of Saturday's game and refused to discuss Mackay's position.
After being appointed manager, Mackay led Cardiff to the League Cup final and Championship play-offs in 2012 before masterminding their promotion to the top flight of English football for the first time since 1962.
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