The Bluebirds secured top-flight football with a goalless draw at home against Charlton Athletic this evening.
Hudson, 31, said that he and his teammates will allow themselves to celebrate before refocusing for the final three games in order to win the title honours.
"I am lost for words right now," Hudson told BBC Sport.
"We thoroughly deserve that, if I'm honest. The consistency we've had this year, top since November, and now we're promoted.
"We'll celebrate now then go for that title."
Hull City and Watford will contest the last automatic-promotion spot.