Pogba said Rudiger had “nibbled… a little bit on me” but should face no punishment.
The Germany defender appeared to make contact with his mouth on France midfielder Pogba’s back in Tuesday’s Group F opener.
Manchester United man Pogba initially reacted in shock, but later insisted Rudiger should face no punishment.
Rudiger has now moved to clarify the situation, insisting he did not bite Pogba, and the Chelsea defender is understood to harbour regrets over the incident.
“I should not come close with my mouth to his back, no doubt about it,” Rudiger said.
“It looks unfortunate. Paul and I have talked about it as friends after the final whistle.”
Referee Carlos Del Cerro Grande and his team of officials took no action during the Munich encounter, and Pogba quickly insisted after the match that he agreed with that stance.
“I’m not crying for cards, yellow, red cards, because of such actions,” said Pogba.
“He nibbled, I think, a little bit on me. But we have known each other for a long time.
“I told the referee and he takes decisions and he took a decision. It’s over.
“It was a great match for us, and I didn’t want him to be suspended because of such a situation.
“It was towards the end of the match. We hugged each other and that’s it.”
Reigning world champions France got their campaign off to a positive start thanks to an own goal from Germany defender Mats Hummels.
Kylian Mbappe and Karim Benzema both saw strikes chalked off for offside and Adrien Rabiot struck the outside of a post as Les Bleus pushed for a second.
Thomas Muller, Ilkay Gundogan and Serge Gnabry could not capitalise on openings for Germany in an engaging contest.