"I did feel I was going to lose my job on the weekend," said Mackay, "The email deeply upset me. I declined to resign and expected to be sacked."
“I don't know if we can talk... ”
Malky Mackay on Vincent Tan
The departure of Mackay, who guided Cardiff to promotion last season, looked imminent after the defeat at Anfield.
But then Cardiff chairman Mehmet Dalman released a statement on Sunday that indicated he would remain in charge for the "foreseeable future".
Dalman is trying to repair the fractured relationship between manager and owner.
Tan, a 61-year-old businessman from Malaysia who bought a controlling stage in Cardiff in 2010, is understood to be unhappy at an apparent overspend on players and has also been critical of Cardiff's style of play.
Dalman hopes Tan and Mackay will meet for talks soon, although Mackay said the meeting might not take place until the end of the week.
"I wanted that meeting to be today, but that was declined," said Mackay at a news conference on Monday. "If not today, then tomorrow, but that was also declined."
He also admitted he was not sure if there would be a reconciliation.
Mackay thanks Cardiff fans following the 3-1 defeat at Anfield on Saturday
"I don't know if we can talk," he said. "Mehmet has been trying to do this for three months, as have I.
"I will find out when I go to the meeting. At that point, I will take stock of where I am."
Mackay, who has been in charge of Cardiff since June 2011, praised Dalman as "a good man and a sensible man" but pointed out that he was "not the man who makes the decisions".
The former Watford boss added: "There is no more pressure on me now. The team are working so hard and have come up with reasonable performances and good results.
"I'm proud to be the manager here and I think I should be the manager.
"I will keep doing what I'm doing. If someone wants to do something different, that's up to them."
Cardiff currently sit 15th in the table, four points above the relegation zone, and face Southampton at home on Boxing Day before welcoming bottom of the table Sunderland to Cardiff City Stadium on Saturday.
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