Morgan and Moxey have so far drawn a blank in replacing McCarthy after failing with approaches to the likes of Alan Curbishley, Brian McDermott, Gus Poyet and Walter Smith.
Connor will be in charge of the side at Newcastle on Saturday, and said: "They have to make the right decision. They are the custodians of the club. It's up to them to take whatever time it needs to make sure the club moves forward."
He added: "Just because something doesn't happen in one day as the media or fans would like, it doesn't mean they should rush into something they may regret later down the line.
"The next appointment is crucial, whether it is for 13 games or the next 13 years.
"You have to give them the benefit of taking that time and finding the right candidate to do the job, whether as a short- or longer-term project."
Connor is refusing to say if he would like to be considered for the post but admits being a manager will appeal to him at some juncture.
He said: "I have worked all my life to try and better myself. I've been a player, youth team, reserve team, assistant manager and been on my courses for management.
"I've worked towards possibly being a manager someday but right now I'm employed now by the club as assistant manager.
"They want to appoint a new manager and I'm just looking after things until decisions have been made. The club have asked me to look after it until Saturday. Let's just go to Saturday and see what happens."
Source: PA
Source: PA