The 32-year-old sprinted 30 metres up the pitch and slid into the back of Stoke winger Ibrahim Affelay, who was shepherding the ball out of play near the halfway line.
O'Neil took to Twitter to make amends after the match, saying: "Apologised to all the lads & the staff @Ncfc. Massive apology to all fans as well! Made a big mistake. Out of character. Won't happen again."
Manager Alex Neil offered no defence for the midfielder's actions, saying he was as "surprised as anyone" by the tackle.
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"There is no defending it. It was certainly a sending off and Gary apologised to his team mates at halftime," Neil said.
"We were pleased with how the game was going but that was a big turning point, it gave Stoke an advantage.
"It was completely out of character but to make that decision in such an important game was silly to say the least.
"He knows he's done wrong. Me slating him isn't going to help anything and we're going to miss him for three more games (through suspension) as well."
The defeat left Norwich in 15th place in the table, five points above the relegation zone, while Stoke rose to seventh.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
