The two players battled it out as France defeated Germany 1-0 in their opening group game of Euro 2020.
An own goal from Mats Hummels settled the game.
During the clash, video footage showed an incident where Rudiger appeared to try and bite Pogba in the back during a physical altercation.
"With Tony, we are friends," said Pogba post-game.
"This was nothing big. I think you saw the TV pictures, this is all over, this belongs to the past, I'm not crying for yellow or red cards for such actions.
"He nibbled, I think, a little bit on me, but we've known each other for a long time.
"He hasn't received any card, I think it's better like this. I don't want him to be suspended because of such a situation. At the end of the match we hugged each other and that's it."