"When we win, the heat is off. When we lose, the heat is on. That's just our business, that's our society, that's New York," Anthony said after scoring 30 points in an 83-78 win over the Chicago Bulls on Wednesday night. "It happens. He can't worry about that. We can't worry about that."
Anthony and the Knicks gave Woodson some breathing room with the win over the Bulls.
New York (6-15) is performing well below preseason expectations, though.
Woodson's club had lost 11 of its previous 13 entering play Wednesday, so there was speculation prior to the game that Woodson's job was in danger.
Owner James Dolan gave Woodson a public vote of confidence Nov. 20.
But the Knicks have gone 3-7 since Dolan's comments, including a 41-point loss to the Celtics on Sunday and a 15-point loss to the Cavaliers on Tuesday.
A league source with knowledge of the coaching staff's thinking told ESPNNewYork.com on Tuesday that there had been a shift from Dolan's stated vote of confidence in light of all the losing.
Last week, the New York Post also reported Dolan's confidence in Woodson had waned.
It is unclear whether Wednesday's win had any effect on the organization's thinking.
Coaching sources told ESPN.com's Marc Stein after Tuesday's loss that Woodson is more concerned about his job security than he has let on publicly. In numerous interviews on the subject, Woodson has put on a brave face, insisting he is focused on nothing more than trying to dig the banged-up Knicks out of this hole.
Woodson also has said publicly that he never worries about job security.
"I have been at this thing 30 years," Woodson said in an interview on ESPN New York 98.7 radio last month. "And the one thing I never and will never do is look over my shoulder. I won't do that. I got too much pride for that."
Following New York's nine-game losing streak, Anthony acknowledged he and other Knicks players were concerned Woodson would lose his job.
"Yeah, we're worried about that. But then again, we've got to worry about playing basketball, man," Anthony said last week.