Rose was taken off in the 70th minute of Spurs' 3-0 Champions League win at Wembley on Wednesday night after a tussle with Apoel's Roland Sallai left him needing stitches around the top of his left eye.
After returning from nine months out with injury in October, Rose is desperate to regain fitness and he reacted to his withdrawal by marching straight down the tunnel, before re-emerging soon after to take his place on the bench.
The episode looked fairly harmless but Rose has become a magnet for controversy in recent weeks.
After his explosive interview in August suggesting he wanted to leave Spurs, the 27-year-old admitted last month he was "fuming" with Pochettino for leaving him out of the squad to face Arsenal.
Rose, however, insisted there was nothing in this latest incident and is fed up with talk of a rift.
"This is getting silly now, the manager said it was best I came off and I didn't want to come off. That was it," Rose said.
"I've seen already that people are saying we exchanged words. There is no issue between me and the manager. There has never been an issue. And people trying to put stuff in the media is not welcomed.
"For the last three-and-a-half years, four years, the manager has been my biggest fan. He's given me nothing but love and respect.
"There is no issue. There never will be an issue. People need to stop this because it's not welcomed."