The Portuguese forward came on as a substitute in the first leg of the Supercopa de Espana and scored a long-range effort to edge his team back into the lead.
However, Ronaldo was sent off two minutes later after picking up a second yellow card for seemingly diving after going down under pressure from Barcelona defender Samuel Umtiti.
Ramos, whose side won the game 3-1, told reporters: "I was far away, but I think it was a piece of play in which [Ronaldo] lost his balance, rather than feigning anything.
"It could be appealed. Sending off a key player with 10 minutes remaining of a Clasico in which we've given our all is something which needs to be evaluated and thought about."