The decision by referee Kevin Friend provoked a storm of criticism after Brown appeared to win the ball and not even touch Potters 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 on Tuesday.
A Black Cats 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.
- Sports & Recreation
- the Football Association