Ramos urged Atletico head coach Diego Simeone to teach Griezmann some "values" after the Frenchman and World Cup winner talked up his Ballon d'Or chances.
Atletico forward Griezmann and Ramos went head-to-head in Saturday's Madrid derby, which ended goalless at the Santiago Bernabeu.
Asked about Ramos afterwards, Griezmann said: "He's my little friend, I have a lot of respect for him.
"He's an example for the kids and a great centre-back.
"For me, this is a game, I like to have fun with my team-mates and with players from other teams.
"Sometimes I'm 'poking' and this time I was 'poked'."
Ramos also discussed Griezmann following the clash and the Spain international told Movistar Plus : "I have not spoken with Griezmann, regardless of the opinion of each other, one must always have the utmost respect for a fellow professional."
Barcelona and Madrid are level on 14 points atop the LaLiga table, two points ahead of fourth-placed Sevilla.