Stoudemire has had three knee surgeries over the last 12 months so the Knicks are taking a cautious approach with the six-time All Star.
He is playing on a minutes limit of 10 per game and will not play in both games of a back-to-back. Woodson hopes to alternate Stoudemire and veteran forward Kenyon Martin when the Knicks play back-to-back games. The coach also may alternate between Stoudemire and Martin on a game-to-game basis.
Stoudemire on Saturday said it is difficult to sit out games when he feels healthy enough to play, but he understands the team's rationale.
"It's not easy when you're known for being a superstar player and then having to accept the role of coming off the bench and then also limited minutes, it's never easy," Stoudemire said. "It's definitely a process that you have to mentally prepare yourself for. But at the same time it's for the betterment of the team and also it's better for yourself, to prepare yourself to heal and be ready for the [long run]."
Stoudemire sat out of the Knicks' season opener against Milwaukee on Wednesday and played 11 minutes in a loss to Chicago on Thursday. He expects his minutes limit to increase as long as he stays healthy. But he doesn't feel the need to push to play more minutes at this point.
"Right now it's only game two, there's no rush," he said. "We're playing well. We're still solid and if they need me I'm here for that extra weapon."
The 11-year veteran played in just 29 regular season games last year due to recurring knee issues. He underwent arthroscopic surgery on both knees to clean out debris.
Stoudemire also had microfracture surgery on his knee in 2005.
Due to injuries, his five-year, $100 million contract with the Knicks is uninsured. He has two years and $45 million left on the deal.
Ian Begley is a regular contributor to ESPNNewYork.com.