David Kerslake and Joe McBride will remain in temporary charge of the Cardiff team against Arsenal on New Year's Day.
Kerslake made it clear he has no aspirations to take the full-time job.
David Kerslake: "I have been in the position for six hours and had three phone calls from the director, one from the chief executive, one from the chairman and one from the owner. That's probably put me off for life!
"They were all well wishes as well, by the way, but I have been a coach for 10 years. I love what I do. I love being on the grass with the players.
"The players are devastated in the dressing room. We got ourselves in a fabulous position and we should have seen the game out.
"It is disappointing for us because we were 2-0 up. With eight minutes to go, we conceded a poor goal so there is work to be done.
"The players found out (about Mackay) via the TV. I guess they are only human and they have probably been on the phone talking about it.
"The way we came out the traps today they certainly put it behind them.
"The manager has asked for that start for the last two-and-a-half years and to come out all guns blazing. For 35-40 minutes, we blew Sunderland away."