Woodson revealed Tuesday during an interview with ESPN New York 98.7 FM that Anthony had asked to be removed from the game due to knee discomfort before suffering the injury in the second quarter.
Woodson decided to leave Anthony in the game against the Cleveland Cavaliers, and the All-Star aggravated the knee injury after tripping without contact. Anthony went to the locker room with 6:42 remaining in the second quarter and did not return to the game, as the Knicks rallied from a 22-point deficit to win, 102-97.
The Knicks announced later Tuesday that Anthony officially has been diagnosed with a sore knee and will be listed as questionable for Wednesday's game against the Detroit Pistons.
At Wednesday morning's shootaround, Woodson told reporters that Anthony has a buildup of fluid on his knee and will be a game-time decision for the game against the Pistons. Anthony was at the team hotel receiving treatment on the knee during the shootaround.
In Tuesday's interview on "The Stephen A. Smith and Ryan Ruocco Show," Woodson called Anthony's injury "alarming" and admitted his decision to leave the star forward in the game was "stubborn."
"Melo was hurt," Woodson said. "For him to ask me to come out of the game before he actually took that spill made me realize that something wasn't right. He's never ever, ever, even hinted about coming out of the game [before Monday]. I play him too much in that regard. Melo's a trooper -- he's a warrior, he's a tough kid."
Woodson was asked during the interview why he chose to leave Anthony in the game after he requested to come out.
"I should have [taken him out]," Woodson said. "Stubborn coach -- I just didn't."
Woodson explained that he hoped Anthony would help dig the Knicks out of their 22-point first-half deficit.
"Maybe I should have taken him out before he actually stumbled and took the fall," Woodson said. "But again, I'm thinking [during] the game, 'Hey, he'll play through it. He'll figure it out.'
"But he was hurt. He walked out after he took the spill and he didn't come back, and that's not Melo-like. Obviously, his knee is bothering him."
Anthony said on Monday that his knee had been bothering him in recent days, and an MRI taken recently revealed no structural damage.
"Today I just woke up, and you know how some days you really don't feel right," he said after the game. "I came out here and I tried to warm up and I thought it was going to loosen up before the game, but some of the things that I was doing, I felt like I was dragging it."
Knicks general manager Glen Grunwald said Tuesday in an interview with radio station WFAN that he did not believe the injury was "serious," even though Anthony has been bothered by the knee for two or three weeks.
"We're going to try to be smart about it and we're not going to rush him along if we don't think it's appropriate," Grunwald told WFAN.
The Knicks have not planned further tests on Anthony's knee. The 28-year-old Anthony is the NBA's second-leading scorer at 28.2 points per game.
Ian Begley is a regular contributor to ESPNNewYork.com.