The 20-year-old came through the youth system at the Stadium of Light and into the reserves, but after failing to break into the first-team squad, the playmaker moved to Carlisle on a permanent transfer in January.
Noble took to Twitter and said: "Sunderland was great until I signed a pro contract. Only one club gave me a shot at pro football. Many thanks to everyone at Carlisle United. Great club great fans.
"Not bitter at all about leaving Sunderland! Sh*t club sh*t fans! Hope to see you's soon. Maybe give us a derby next year. Haha."
Reports have claimed that Carlisle are pondering whether to take disciplinary action against the midfielder for his comments.