Watson - the last man to lift silverware for the Toffees in 1995 - is now a coach at Newcastle United.
“Michael has done very well this season, he is taking on the responsibility of being the main man in the middle of Everton's back four," he told evertonfc.com.
“That is a big change for any defender, rather than looking for help from someone next you, it becomes your job to guide players.
“He is gaining experience and will become an even better player with more international matches.
“I think he has been great this season and I am sure there is a lot more to come from him.
“And with the confidence he's gained recently, he will feel the same."