The Everton caretaker manager is still waiting to see whether he will get the job permanently.
Unsworth has been in caretaker charge of Everton since the dismissal of Ronald Koeman last month and the 44-year-old has overseen some woeful performances and results, including the 4-1 defeat to Southampton at the weekend.
As reported by Reuters, Moyes said: “If he doesn’t take the Everton job, I think I would be telling Unsy to go and manage somewhere and earn your corn.
"If you want to move on, go and get a job in the Championship or League One. I think there has been a generation of really good players out there who I believe should go and manage and try and come up.
“I would say earn your stripes first and show you can organise so that you can control the team and show that your training works, all the things that are linked with management and leadership.”
Unsworth earned much praise for the work that he did with Everton U23s, whom he guided to the Premier League 2 title last season.
However, the former Everton player has certainly found the step up to management at senior level rather difficult, with the club's unbalanced squad certainly not helping his cause.
Former England and Crystal Palace manager Sam Allardyce is the leading candidate to take charge of Everton, as reported by BBC Sport.
If Allardyce is appointed then Unsworth could well leave Everton, although it remains to be seen whether he would be cut out for a full-time management position, even in the lower leagues.