The Spurs cruised to a 120-89 triumph at Madison Square Garden on Sunday.
When asked if his team had shown any pride as their challenge faded in the second half, Woodson told reporters: "No. No. Not at all. It's something that will be addressed.
"It's just unacceptable. It's my job to push them through it and try to get them over the hump.
"I know we're a better team than what we've shown. We didn't compete tonight. That's just unacceptable."
The Knicks will aim to recover from the defeat when they face the Atlanta Hawks on Wednesday.