The 26-year-old Scotland international claimed just his third goal of the season to inspire a late fightback at Cardiff on Saturday evening as the Black Cats claimed a 2-2 draw to go with their Boxing Day victory at Everton and boost their hopes of escaping the drop from the Barclays Premier League.
Speculation has suggested that Fletcher, a £12million signing from Wolves during the summer of 2012, could be a target for potential purchasers when the winter transfer window opens on Wednesday, but Poyet is planning to have him at the pinnacle of his team.
He said: "There are positions on the pitch, with respect to everybody, of course, and every single player, that are key in any team.
"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."
Poyet's favoured system includes just one frontman, and Fletcher and United States international Jozy Altidore have tended to alternate with their appearances together to date having yielded limited results.
But with the threat of relegation a very real one, the club are currently two points from safety, the Uruguayan admits he needs to design his team to get the best out of the Scot.
He said: "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 or better to play with a player around. It's understanding."
As far as Fletcher leaving Wearside is concerned, Poyet insisted there has been no formal approach for him, or indeed any other player, as yet.
He said: "We haven't had any offers for any players. If somebody wants any player from the club, playing or not playing, the only thing they need to do is make an offer because there is no way that we are going to be talking about individuals.
"It's just waiting."
Poyet's squad will be boosted on January 1 when Fiorentina left-back Marcos Alonso joins the club on loan for the rest of the season.
The manager said: "I can confirm Marcos is going to be with us for the rest of the season on loan from Fiorentina, which is something very important.
"I was always looking for a player in that position on the left side and I hope he will help us and everybody will like him.
"I am delighted that everything is agreed."
Alonso is unlikely to be the last arrival before the end of next month with Poyet targeting up to four new signings.
He said: "The problem with the number is if you tell me how many we need, it would probably be a list. Three or four?
"It's so unpredictable either way because when somebody comes in, somebody starts feeling that he doesn't have a place, or if you sign a player in a certain position, the rest think it's because of them.
"I am just making sure that we are ready and we have got options for anything that happens. But initially, yes, I would say the number is around four."