The Toffees take on Wigan Athletic tomorrow for a place in the semi-finals of the FA Cup, which they have not won since 1995.
"It has been too long," BBC Sport quotes Baines as saying. "It is the one thing that is missing for [Moyes] and the club. The manager has been at the club for a lengthy spell and silverware would cap what has been a good spell for him."
Meanwhile, there have been doubts over Moyes's future at Goodison Park following revelations that he will not discuss a new contract until the end of the season.