Everton boss Moyes challenges Jagielka to become England first-choice
Moyes intends to make Jagielka club captain next season when Phil Neville leaves the club.
"Jags was top drawer against Liverpool and he has been like that for a long time," said Moyes. "He sometimes doesn't believe in himself enough or have the confidence he should have when you see how he plays.
"But when you look at the situation with England at the moment, it's there for Jags to go and say 'pick me'. As a manager he gives you everything.
"He didn't train much this week because he had a thigh strain but that just shows you, all credit to him.
"He's been absolutely superb for us - he can be a real leader."