An early own goal from Sunderland skipper John O'Shea was added to after the break by an effort from Jon Stead to help Phil Parkinson's men onto a 2-0 win and a place in the quarter-finals.
In truth, City had the upper hand for most of the match and always looked the more likely winners thanks to a strong and determined display from Parkinson's men.
And backed by their amazing home support, City certainly more than merited their latest Premiership scalp in the eyes of Knott.
Knott, who left Sunderland in the summer, said: "We fully deserved that today (Sunday). The boys were fantastic.
"We stuck to our game-plan and we deserved this win. I think the Sunderland fans knew that by the way they clapped us off at the end.
"Our fans were fantastic as well today. When they turn up like they have for this game, it is hard not to perform in front of them. I don't think anyone can deny that this was a well-deserved win for us.
"This has been a brilliant day for the club and I have to thank the fans for their support once again.
"We started bright and we were on it right from the beginning.
"It was a great win and a deserved win."
After the joyous scenes of Sunday and the Sunderland win, Knott and his team-mates can now look forward to a return to Sky Bet League 1 action at Leyton Orient this Wednesday.
Knott added: "We have an important game in the league now on Wednesday at Leyton Orient.
"We will enjoy this (Sunderland) win but our thoughts will quickly turn to Wednesday again.
"It is a big match for us and we want to keep going in the league. We will be focused on that.
"The cup run is nice for the club and we have confidence we can take on anyone but the most important thing now is the league and Wednesday. We want to be climbing back up that table."