"That's no reflection on Sam, that's just the way I have always done things.
"But for once in my life I ignored my intuition and, looking back, that was a mistake."
Newcastle had hoped to bring in Portsmouth manager Harry Redknapp to replace Allardyce who left the club after only eight months in charge.
But Redknapp said on Saturday that he had rejected Newcastle's "terrific" offer, and the club are still searching for a new manager.
Ashley, who is famed for wearing a replica Magpies shirt and sitting with the fans despite his vast wealth, says now is the time to take a more hands-on role at boardroom level.
"Now is the time to put away my Newcastle shirt," he said.
"I'm not saying I will never go back on the terraces, but now I have to be in the boardroom - I have to be hands on."
He said he is desperate to bring silverware to St James' Park, but more importantly he wants to see exciting football at Newcastle.
He said: "I want a team that will go all out to try to give Chelsea a walloping, that will try to stuff Tottenham and that will be brave and bold enough to attack Manchester United."