The boxer is preparing to face Alexander Povetkin at Wembley Stadium on September 22.
He owns three of the four major belts in the heavyweight division as he looks to become the unified champion.
The biggest challenge to his rise came against Klitschko in 2017, where he was knocked down in the fifth round.
But Joshua got back up again and finished off the Ukrainian in the 11th round, knocking him down twice.
Footage has now re-emerged of the boxer appearing on Conan O’Brien’s American chat show where he talks about that fight.
In the clip, Conan asks the IBF, WBA, IBO and WBO champion what it is like to be hit in the head.
“It’s interesting because it’s the last thing you get taught, to be hit,” Joshua says.
“There’s no coach that will come into the gym and tell you he’s going to hit you with a baseball bat – train yourself to deal with it.
“It becomes a situation where it’s fight or flight. Either you get up and continue or you don’t have it in you. You find out on the night you’re in the ring.
“I was down and out in that fight but I got up, continued and was victorious.”
But when Conan continues to ask the heavyweight about the knockout, Joshua comes out with a hilarious line.
“What really happened is I slipped,” he said.
“It looked like he punched me and I’m going to keep saying that until everyone in the world believes it.”
But the host is equal to it, replying, “Yeah, you slipped and fell onto his glove!”
All the 28-year-old can do is laugh and look down at the floor.
The clip first aired on US network TBS on May 23.
It has now re-emerged on Reddit after Deontay Wilder, who holds the WBC belt which would finish Joshua’s collection, was reportedly set to fight Tyson Fury in December.
And boxing fans have now pushed the British-born Nigerian to fight the American.
“Anthony Joshua v Deontay Wilder needs to happen,” one viewer wrote.
Another added, “Joshua v Wilder 2018!”
While a third simply said, “Joshua vs Wilder, when aggression meets tactical.”
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