Poyet's men put in an improved performance following last week's 8-0 humbling at Southampton when hosting Arsenal at the Stadium of Light on Saturday, only to be undone by individual errors.
Wes Brown and Vito Mannone were at fault for both goals, their mistakes gifting Alexis Sanchez a double.
Poyet now has nine days to get his men back on track as Sunderland attempt to add to their solitary Premier League victory this term when they tackle Crystal Palace a week on Monday.
The manager said: "It is a long week because we play on Monday but lifting the players is part of the job.
"We are getting paid to win games and we have won just one. It is time to win again."
Mannone, in particular, will come in for criticism having struggled at St Mary's and then dawdled on the ball on Saturday to allow Alexis to wrap up the result late on.
Poyet, though, refused to be drawn on the goalkeeper's form, saying: "I will be assessing everybody's mood. I think that is important."
