The decision by referee Kevin Friend provoked a storm of criticism after Brown appeared to win the ball and not even touch Stoke midfielder Charlie Adam.
Sunderland confirmed they have lodged an intention to appeal against the decision with the Football Association and will send in a full appeal file before a deadline of 1pm tomorrow.
A Sunderland spokeswoman told Press Association Sport: "We have lodged our intention to appeal against the decision."
Sunderland lost the match 2-0 and manager Gus Poyet demanded an apology from Premier League referees chief Mike Riley.
Meanwhile, former Premier League referee Dermot Gallagher believes Friend made a clear mistake.
He told Sky Sports News: "I can keep this very short. We have to take it smack on the chin. The referee has lost concentration or not seen it.
"It is not a red card, that's all you can say.
"Brown's gone in hard but he's entitled to do that. As a refereeing body you have to take that smack on the chin."
After a weekend full of controversial decisions, Gallagher also felt Phil Dowd had made a mistake in not sending-off Everton's Kevin Mirallas for a wild lunge on Liverpool's Luis Suarez in the Merseyside derby.
"He should have been sent-off," said Gallagher. "He's come at speed and it's high.
"The referee has got a body between him and Suarez and he hasn't seen it."