The Scotland international has scored just twice this season, with his last goal coming in the 2-1 derby victory over north-east rivals Newcastle in October.
But Poyet insists the former Wolves striker, who has scored less goals this season than Sunderland full-back Phil Bardsley, has not been given a proper supply line.
"If he had missed a clear chance, I would have to say maybe he was lacking confidence, but he hasn't had too many because we are not creating too many," Poyet said.
"We are missing the last pass, cross, decision, movement. That's been missing. It's the most difficult part of any team, any game.
"There are plenty of teams out there who are decent up to a point, and then after that, you are missing that last punch and we are no different at the moment."
Sunderland are bottom of the Premier League and visit Upton Park after successive home defeats to Chelsea and Tottenham.
And Poyet acknowledged his side will be boosted by the absence of Stewart Downing and Andy Carroll for West Ham through injury, and Kevin Nolan who misses the game through suspension.
"I am sure if you are playing Barcelona, it's better if Messi doesn't play, and if you are playing against Real Madrid, it's better if Ronaldo doesn't play," Poyet said.
"They are very important players, so it's an opportunity. But I am sure the players who will play are Premier League players who are going to give 100 per cent for West Ham.
"But we will see. On paper, it could be better, but we need to play the game the same way because they are Premier League players."