Fletcher has endured a difficult time with injuries after missing the start of this season and the last two months of last term with an ankle problem.
The Scotland international scored on his return to action against Crystal Palace at the end of August before picking up a shoulder problem which sidelined him for three weeks.
The former Wolves man returned from injury to score against Newcastle last month and Poyet is confident Fletcher will show his true worth once he gets a run of games under his belt.
"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," Poyet told the Sunderland Echo.
"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.
"We have to remember that he was out for a long time, came back, got injured again and is only now coming back once more.
"It is unfair to put too much pressure on him too soon - it is only a matter of time before he starts scoring regularly for us if he stays injury-free."