The 67-year-old Dutchman will head into Tuesday night's Capital One Cup third round clash with Manchester City at the Stadium of Light having seen his side fail to win any of their opening six Barclays Premier League games of the season to sit at the foot of the table.
Asked if he had any regrets about deciding to shelve his retirement plans during the summer, he replied: "No, no regrets.
"Listen, let's be clear: if I feel that it is better that somebody else takes over, I'm the first man who will say, 'It's better for the club, I will go', believe me."
They will attempt to steady the ship against the Premier League leaders, who beat them in the League Cup final at Wembley in March 2014, with Advocaat keen to further annoy opposite number Manuel Pellegrini.
He led Russian side Zenit St Petersburg to an aggregate victory over Pellegrini's Villarreal in February 2008 on the way to UEFA Cup glory, and the Chilean was not happy about it.
Advocaat said with a smile: "When I was the manager of Zenit, we played against Villarreal and I kicked him out of the UEFA Cup, and he was very angry because he did not expect that.
"He's a very, very nice man."