After the match, Poyet said that the win was "important" as his players adapt to his style of play. However, he also called on them to stop conceding.
"We are desperate to see the team play in a good way. It was important for the players. It's a new way, a different way. We can do it. It's just started, it's the beginning," he told BBC Sport.
"We need to make sure we are a very strong at home. You have 40,000 people behind you at home. We need a clean-sheet now."
Sunderland will play Chelsea in the quarter-finals.