The Manchester United star reacted with a grimace and asked referee Carlos del Cerro Grande about the contact, though neither the official nor VAR Juan Martinez Munuera took any action.
Pogba said after the game that he felt Rudiger 'nibbled' him rather than performed an outright bite, and stated that he didn't want the centre-back to face any potential retrospective punishment from UEFA.
On Wednesday, UEFA said it was not opening a disciplinary case against Rudiger, and the defender - who had said before the game that his team would need to be "disgusting" to beat the world champions - admitted he shouldn't have gotten so close to Pogba.
"I shouldn't go like that with my mouth to his back - no question - it looks unfortunate," Rudiger said. "Paul and I spoke very amicably after the final whistle, and he confirmed to me and then again in an interview that it wasn't a bite, like one or other outsiders said at first."
After the game, Pogba had said of Rudiger: "He nibbled, I think, a little bit on me. I felt it, I told the referee, and he makes the decisions, and he took a decision. It's over. I just want to play football. He hasn't received any cards. I think it's better like this."
But Pogba added: "I am not crying for cards, you know red cards, because of such actions."
In 2014, Uruguay forward Luis Suarez was retrospectively banned for nine games by FIFA after biting Italy defender Giorgio Chiellini at the World Cup, leaving the Italian with teeth marks on his shoulder.
Additional reporting by AP.