The Dutch left-back marked his comeback from a shoulder injury that has kept him out since November by scoring the only goal of the game as Sunderland beat Leeds United 1-0 in the FA Cup third round at the Stadium of Light.
Van Aanholt's performance should serve as a boost to a Sunderland side that sit 14th in the Premier League and will be looking to pull away from the relegation fight in the second half of the season.
Poyet conceded that it has been a frustrating spell on the sidelines for Van Aanholt but stressed that it was the correct call to allow the former Chelsea man the proper amount of time to recuperate.
"It's been difficult for Patrick missing so many games, but at the same time he needed to sit out and recover properly," Poyet told Sunderland's official website.
"When any player is out with an injury we always look forward to them coming back so it's very nice to have him back in the squad."
Sunderland switch attention back to Premier League action on Saturday when they welcome Liverpool to Wearside.
