Craig Mackail-Smith, Ashley Barnes and Stephen Dobbie have not found the net in the Seagulls' last four outings.
Poyet said: "Someone needs to score. The strikers need to play for the team, understand the way we play and help the team, but at the same time score and help us win the game.
"These are the things we need to put into consideration and if they have the chance they need to play their game. If everything goes alright they are going to have more chances.
"In my group of players there are not many who are really ahead of the rest. They are very similar and if they are performing well they have the chance to be in the team in front of someone else. It's completely up to the players.
"I say to them 'show me what you can do, but show me for the team'. Without playing for themselves they need to start producing because they are playing in very specific positions. They need to score goals."