Rodwell, signed from Manchester City this summer, made his debut in the Premier League season-opener against West Brom, which finished in a 2-2 draw.
Poyet – who substituted him after 68 minutes - was satisfied with the midfielder’s performance but says Rodwell’s team-mates learn to play to his strengths.
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."
Poyet was pleased with his team’s resilience, with the Black Cats going 2-1 down before Sebastian Larsson scored an equaliser five minutes from full-time.
He said: "Last year, after conceding the second goal, maybe we would have collapsed and conceded three or four.
"There is a little bit better, stronger mentality in the team.
"If you see the reaction of the players on the pitch when we score and the celebration, coming back and trying to go again, I think it is a good sign for the future."