Poyet's men face a stiff task to claim a result at Anfield on Wednesday, with Liverpool seeking a seventh successive Premier League victory to move within one point of leaders Chelsea.
|18/1||Connor Wickham is 18/1 with bet365 to score first v Liverpool|
"We've been trying different things, different situations," Poyet told reporters. "Fabio is not available, so I'm going to keep trying different things.
"Connor is an option. I can't keep closing my eyes, keep picking the team until the end of the season and think why didn't I try that.
"It's my job to keep searching for the solution and then you know you've done everything."
Poyet believes a lack of expectation could work in Sunderland's favour at Anfield.
"We need to be a very good team because [Liverpool] have been scoring for fun," he added.
"We need to change that goalscoring situation somehow. At different times during the game, they're going to be pressing, especially with the excitement around Liverpool right now.
"No-one expects us to do anything. But we've got a chance to go there, relax, play our football and defend well."