The Bavarians appeared to be in an unassailable position in Saturday's clash with Fortuna Dusseldorf, leading 3-1 with 15 minutes left on the clock thanks to a Thomas Muller double and a goal from Niklas Sule.
But the visitors had other ideas, with Dodi Lukebakio charging back to score two late goals and complete his hat-trick as Bayern were forced to settle for a 3-3 draw.
Kovac is now under serious pressure in his first season in charge, having led Bayern to just six wins in their opening 12 league games to allow Borussia Dortmund to race away at the summit.
"Today is a difficult day for us," he said to Bild after the match.
"There is a need for internal discussions. But on Tuesday our coach will definitely be called Niko Kovac."
Hoeness was particularly withering over the Bayern defence, as he failed to hide his fury at dropping two more points.
"What I saw in the first goal I know only from slapstick comedy films," he fired.
"That is surreal. I feel like I am in a bad film."
Bayern now trail leaders Dortmund by nine points as they languish in fifth place in the Bundesliga.
Kovac and his battered troops host Benfica on Tuesday, before continuing their faltering league campaign away to Werder Bremen next Saturday.