Reports immediately after the match suggested that Hockaday would be losing his job after three defeats out of four already this season.
And Cellino confirmed that firing the manager was certainly his intention following the match - but a chat between the pair had led him to change his mind.
He was quoted as saying: "Yes, I decided to sack him. I said, 'He's finished.' But I learned a long time ago to wait on a decision for 24 hours.
"If I fire the coach I should fire myself because I haven't signed enough good players. How can that be his fault?"
The Leeds job is Hockaday's first managerial post in the Football League, while Cellino's eccentricities have long been noted.
Cellino earned his unflattering nickname of the 'manager eater' during his time in charge of Cagliari, where he went through 36 managers in 20 years, and he has already looked to pull the trigger during his short time at Leeds.
He attempted to sack then-manager Brian McDermott within hours of verbally agreeing a deal to buy a controlling stake in the club with GFH Capital at the end of January.
McDermott stayed until the end of the season and departed by mutual consent at the end of May.
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