The 69-year-old action legend had been the favourite to win the best supporting actor Academy Award for his portrayal of Rocky Balboa in "Creed" but he eventually lost out to Rylance for his turn in Steven Spielberg's historical drama "Bridge of Spies".
In the wake of his loss, Sylvester's brother Frank took to Twitter to blast the Academy's decision to snub his older sibling.
But now Sylvester has taken to Instagram to make his thoughts clear on the matter, posting a photo of him meeting Rylance and writing: "Mark Rylance! Congratulations on your award... Could not go to a more consummate actor and gentlemen. It was a privilege. Keep punching, Mark! (sic).