Parker had run himself into the ground by the time he was replaced by Vedran Corluka in the final minute, leaving the field to a standing ovation.
"It was a fantastic performance," Redknapp told the Spurs website.
"Scott's a proper lad, the type of lad you want at a football club. He's great around the place, a great trainer and great in the dressing room.
"What a performance against Arsenal. He's a fantastic signing for us and will be a fantastic player for this club."