The striker scored 11 goals for Sunderland last season before damaging ligaments in his ankle on international duty with Scotland in March.
He returned in August, netting off the bench against Crystal Palace, but made just three appearances before suffering a dislocated shoulder against West Brom.
Those injuries have limited him to six league appearances and two goals this season, but Poyet is convinced the 26-year-old will find the net on a regular basis if he can stay fully fit.
"Steven Fletcher is a key player for us because he can score goals, and we need to put him in a situation where he can give us that option," the Uruguayan told the Shields Gazette.
"The more he plays, the more he is going to score us goals, and the more he is going to enjoy it.
"He's a real, natural goalscorer, and all he needs is a run of regular games without injury."
Poyet has turned Sunderland's fortunes around since taking over from Paolo Di Canio with two wins in four Premier League matches, but they remain three points from safety.
