Fury, who can be backed at 8/11 with Sky Bet to win the rematch (Wilder 11/10, draw 25/1), said: "We're on away soil, I got knocked down twice but I still believe I won the fight and I believe every man in here thought I won that fight tonight.
"But I'm showing total professionalism here, I'm a true champion and a true warrior. I went to Germany to fight Klitschko, I've come to America to fight Deontay Wilder. Bless Deontay Wilder, he's a top fighting man.
"I was never going to be knocked out tonight. I got put down with some good shots, I showed good heart to get up. I came here tonight and I fought my heart out."
Fury believes he and Wilder are the two best fighters in the blue riband division, pointedly sending a message to British rival - and IBF, WBA and WBO beltholder - Anthony Joshua.
Fury added: "We'll do the rematch but we're going to go away, recalculate, see what's going to happen. We are two great champions. Never mind an anybody, me and this man here are the two greatest heavyweights on the planet.
"I stepped up after the amount of time I had out the ring, there's another certain heavyweight out there. (He's a) chicken - Joshua, where are you AJ?"