The Scotland international claimed just his third goal of the season to inspire a late fightback draw at Cardiff on Saturday to go with their Boxing Day victory at Everton.
Poyet's side remain bottom of the Premier League but with the gap to safety just two points, the Uruguayan is confident of a continued upturn - with Fletcher the driving force.
"There are positions on the pitch - with respect to everybody, of course, and every single player - that are key in any team," Poyet said.
"People talk about the spine of the team - goalkeeper, centre-half, centre-midfielder and striker - but nowadays, I would like to say that everybody is looking for that striker who will score you 20 goals, so the strikers are the main ones.
"That's why sometimes they earn the most and they are most expensive ones to buy.
"Fletch is key, he is a key player for us and we need to make sure that we give him more chances.
"He had one only against Everton and he couldn't score, but then he had one and somehow - I don't know how, still, he stretched himself to score the goal - so we need to put him in there many, many times so that he will score plenty of goals.
"I need to find the balance for him to have chances, yes, no doubt, and that's what we are thinking about.
"Sometimes it is better for him to play with Jozy (Altidore) or better to play with a player around. It's understanding."
Poyet has made one fresh signing in the shape of Fiorentina loanee Marcos Alonso but will hope to prevent key men such as Fletcher heading out of the other door.
"We haven't had any offers for any players," Poyet said. "There is no way that we are going to be talking about individuals. It's just waiting."