The 23-year-old played 68 minutes before being replaced by Jordi Gomez.
Poyet said: "He started well and then we killed him for 20 minutes without the ball. We made him only defend, which of course is going to help us, but we need to give him the ball.
"In the second half I was very pleased - (it was) the Jack Rodwell we want to see, driving with the ball, getting to the edge of the box, winning (the ball), turning, passing.
"I was tempted to leave him on the pitch for a bit longer but I think it was enough and I think he will get better and better."
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