Bill Simmons -- Stephen A. Was NFL's Puppet ... To Smear Tom Brady

Pretty bold allegation from Bill Simmons ... who claims the NFL co-opted several ESPN employees to smear Tom Brady's image during the Deflategate saga ... including Stephen A. Smith.

Stephen A. had tweeted about Brady's 4-game suspension on Wednesday -- saying, "Tom Brady was ARROGANT, UPPITY, SELFISH and in the end he brought this on himself."

That's when Simmons -- who famously left ESPN on bad terms -- chimed in about his former colleague.

"One of multiple ESPN employees used by the NFL to leak anti-Brady info during this saga decides to weigh in."

Gonna guess Stephen A. will have some thoughts on this ...

FYI, we reached out to ESPN -- but the network had no comment.