The Cardiff boss expected to be sacked on the weekend after refusing to quit after receiving an upsetting email from Vincent Tan saying he would fore Malky if he didn't walk.
"I did feel I was going to lose my job on the weekend," Mackay said.
"The email deeply upset me.
"I declined to resign and expected to be sacked over the weekend.
"To give the fans a clap (at Anfield on Saturday) was something I wanted to do for the support they had given me."
But the Scot reiterated he will not be quitting his role.
"If it's anything to do with me I will still be the manager. I won't be resigning from the football club," he said.
Chairman Mehmet Dalman revealed on Sunday that Malky would stay in his job for the foreseeable future as Dalman seeks to mediate between both sides to reach a soloution to the differences.
Malky has asked to see Tan but a meeting has not been arranged yet.
"I have read Mehmet's statement and I've been asked if I will meet Mehmet (and Tan) which is absolutely something that would be for the good of us and the club going forward," said Mackay.
"I think that should be sooner rather than later
"I wanted that meeting to be today but that was declined. If not today, then tomorrow but that was also declined.
"After that we are in Christmas Day and then it's game day so unfortunately it is not gong to be until the end of the week.
"In the meantime I will do my job. That will not change. Mehmet's is a good man and I have found that since he arrived at football club."
He added: "I don't know if we can talk. Mehmet has been trying to do this for three months, as have I.
"There are certain areas that have to be addressed that were in the email. I will find out when I go to the meeting.
"At that point I will take stock of where I am."
Whether Malky and Tan will ever reach a compromise I don't know. It seems that Malky's reprieve in Tan's eyes is temporary. Malky's side must now deliver for him. A bad set of results on the pitch will increase Tan's desire to replace Malky and if the team is struggling the fans may not be so quick to defend him, no matter how much they love and respect him.