Defender Gary Doherty then clinched maximum points for the visitors on Saturday by getting forward to head in a free-kick from Darel Russell.
Poyet moaned: "This is the same old story. A football game is over 90 minutes and you can't give the team at the top a chance to win. It has happened too many times.
"I need to change things. It could be personnel, it could be for us to play a different way. We need to find a solution because we are running out of games."
He added: "The winning goal came from a long free-kick, which should be the easiest to defend. It was not good enough because, as a team, we didn't defend it."