Poyet has admitted that there are defensive concerns to address if they are to stay in the top flight, but insists that there are no question marks when it comes to his team's character and resolve.
"It's difficult to accept, sometimes when you see a team at the bottom they have no spirit, heart and give up," Poyet told Sky Sports News.
"I don't think it's possible to see my team giving up. The downside of the game [is the defending] and we knew that was the way they could hurt us. We will have a few chats about that."
Sunderland have at least one game in hand on the sides around them, and return to Premier League action when they travel to Tottenham Hotspur next Monday evening.