Fury, who many observers believe did enough to win despite being knocked down twice during the fight, said on Monday he feared Wilder would seek to duck a rematch "at all costs".
The big fight placing the Bomber against the Gypsy King took place at the Staples Center in Los Angeles on Saturday, December 1.
Wilder said being more than 50 pounds lighter than Fury at the time of the fight and the after-effects of surgery on his right arm also contributed to his sub-par performance.
"I wouldn't like to go through my career knowing I didn't fight the best". Whenever he's ready, I'm ready. I went to the left. His elbow was out.
And the WBC champion added that he was unable to properly spar as a result.
"We kept that a secret".
"I barely threw any [right hand] punches my whole entire camp".
But even with Joshua holding what he calls his belts, Fury isn't too concerned.
Joshua labels Deontay Wilder a 'fool' after controversial draw against Fury
Fury (27-0-1, 19 KOs), 30, of England, also has expressed interest in having a rematch, and the direct communication between Fury and Wilder is part of what helped the first fight get made.
Earlier this week, Wilder's co-manager Shelly Finkel said the 33-year-old was "very interested" in fighting Joshua.
Wilder said the bright lights of his first pay-per-view fight and a crowd of almost 18,000 fans caused nerves that led him to hunt for a knockout as opposed to staying with his game plan. Like we ain't been interested?!
The controversial nature of last weekend's draw has sparked demands for an immediate rematch and with both Wilder and Fury keen to run it back, Joshua will likely be forced to look elsewhere to find a dance partner for his pre-booked Wembley date next April.
"Anyway well done Fury!"
"I saw my man Joe Hanks [against Joe Joyce] and they got to him quick".
"You thought the first one was something?"
Fury claimed Joshua would have been "nailed" by Wilder, and said his domestic rival has "my belts" - a reference to the titles he held after defeating Wladimir Klitschko in 2015 before relinquishing them due to inactivity.