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Fury maintained his unbeaten record by knocking out his fellow Brit in the sixth round in front of a packed crowd of 94,000.
The 33 year-old reiterated that he was ready to quit after putting on another show in London.
Whyte, who did not feel the referee should have stopped the bout, is hungry for another shot at Fury.
"I should have had time to recover and had time to go back to my corner," Whyte said. "He [Fury] said he'll retire, but hopefully he doesn't retire because I want another go."
Asked what Fury had said to him after the fight: Whyte revealed: "He said 'you're a good fighter, you're a true warrior and you'll be world champion one day,' I'm not a sore loser. You win some you lose some, this is life, this is boxing.
"I showed up and I fought and I gave as many problems as he gave me. It wasn't as if it was a one-way street.
"I'm not one of those guys that want to go out on a loss or a bad performance. I'm still young enough, I've still got a lot left in me. I still feel strong, I'm still getting better. I fought the best in the world and wasn't outclassed.
"He's a bit taller than me, the range is a bit tricky obviously and with the style, it's hard for guys to prepare for him because he's awkward in the way he fights.
"Had I got beat up for four or five rounds and got completely outclassed it may have been time to call it a day, but I wasn't outclassed and it's not a long, hard road back because I showed the level I am.
"We obviously sold 90-something thousand tickets together, it's not him or me alone. I had the value going in before, I'd had loads of pay-per-view fights before and good fights. I'm still here, I'm still good enough, so one fight and I'm back."