The 27-year-old added the WBA heavyweight title to his IBF belt after recovering from the first knockdown of his career to eventually stop Klitschko in 11 rounds at Wembley Stadium.
In only his 19th professional fight Joshua also established himself as the world's leading heavyweight, overcame one of the finest in history and fought in front of a post-war record British boxing crowd of 90,000.
However, despite also revealing the exhaustion he had to overcome to win such a defining and entertaining fight, he insisted it did not represent his peak.
"The memories, the experiences last forever, and when it's all said and done these things (the belts) slowly disappear," Joshua said.
"The experience I've gained is more important than the belts.
"Sugar Ray Leonard: all the skill, ability he had, said there are times when you have to show character and go to the trenches. Without that you'll never go on and do great things in the sport.
"I never want to be in those type of fights, but if I have to be I don't want to crumble."
Asked if it topped winning Olympic gold, he said: "No. It is what it is: there's one winner and one loser.
"I'm a champion outside the ring, first and foremost. The fighting is fun. I don't box just for the belt, for the money, and I just enjoy it, the discipline.
"How am I feeling at the minute? Like I did before I won this fight. I'm happy, if anything, that it was a great fight, because there was a lot of hype, a lot of attention around the fight, and I'm glad it lived up to expectations; that's it.
"I'm going to pop round to my family's house. I want to catch up with family and go back to normal living.
"(I learnt) that I can knock out anyone. If I can keep on improving on the things I do well, I can definitely knock out any opponent.
"To get knocked down, hurt someone, get hurt, take someone out in the championship rounds where I've never been before, it's testament to what training's about."
Joshua knocked Klitschko down in the fifth before celebrating, then tiring himself out by pursuing a stoppage that did not arrive.
He then suffered the heaviest knockdown of the fight after a huge right hand, and remained content to survive until the dramatic 11th round, when he put Klitschko down with an equally big uppercut, before stopping him on his feet after a further knockdown.
"I just said to my coach, 'I took a round off, am getting my breath back and I'm going to bounce back'," he said. "I tried to take him out. When I hurt someone I know I can get them. I know I can get them, so I'm searching, and 'Boom', they were just skimming his face.
"It does take a lot of energy to hit someone hard and hurt them, so I was just fighting too eagerly. I used a lot of energy, so what I did was try to recover, so I could step up again in the late rounds, and that was kind of the gameplan.
"I was definitely tired, but I knew that I could recover and bounce straight back.
"If you get knocked down eight times you get up nine. That's what life's about."