Mitchell had missed the Cavs' past three games with groin tightness and said he felt the issue tighten as he drove to the bucket trying to score a game-tying bucket.
Mitchell remained on the ground after the buzzer, initially clutching his right leg in apparent pain and frustration, before being helped to his feet by training staff and gingerly walking to the locker room.
"I went up to try dunk it, both my legs cramped and my groin just tightened up and locked up on me," Mitchell told reporters.
"Three things happened at the same time. As soon as I jumped, then I tried to get the rebound and that was that."
Mitchell, who finished the game with 24 points on nine-of-24 shooting, said the injury felt similar to his previous groin issue, although he was yet to be assessed.
"It felt the same as before," he said. "I don't know what comes next.
"I felt good enough to come back, and for that to be the last five seconds of the game really pisses me off."
When asked why he stayed on the ground for so long after the game, he added: "It's definitely both [frustration about the injury and his play], but more so [the injury]. I'm praying that I'm all right.
"I screwed that [the play] up. The last few possessions, I can cry about the foul calls all I want. I've just got to be more poised for our group. I had one turnover on a layup, even though I feel like I got fouled, pull it out, run a play, get something.
"Then the second one where I air-balled the layup, that's on me. I let the team down at the end of the game. We played a really good game up until that point, all of us, and I didn't do my job. And that's on me."
The win snapped the Knicks' five-game losing run as Julius Randle led the way with 36 points and 13 rebounds.