He had blamed his unexpected defeat by Tyson Fury in November 2015 - his first for 11 years - on an "off-night", but eliminated that reason here.
Joshua said before the bout that it was just two men in the ring, and nothing more than that.
Joshua said there would be "no problem" if Klitschko wanted a rematch.
"The Bellew fight, we see as, with the right result, will lead Joe into a fight with Joshua". You will probably be surprised by my statement, but I don't feel like I lost. Sometimes you can be a phenomenal boxer but this sport is about character.
Tyson Fury and Anthony Joshua:Who takes the shine?
In the 11th Joshua uncorked a sweet right uppercut to snap back Klitschko's head, followed by another right to send his opponent to the canvas.
Joshua's promoter Eddie Hearn revealed the heavyweight next plans to fight towards the year's end.
"We help out the village she came from and If I could do more on a large scale, I'll definitely come down there and associate myself more with Nigeria", Anthony Joshua added.
Joshua knocked Klitschko down once in the fifth and twice in the 11 before referee David Fields stepped in to protect the defenseless former champion at 2:25 of the penultimate round.
Obamas announce $2-million personal donation to support summer jobs in Chicago
The former President said that might make commutes a bit loner, but will unify the project, like downtown's museum campus. Wednesday's event took place at Chicago's South Shore Cultural Center, the site of the Obamas' wedding reception in 1992.
The pair are training together in Spain but Fury would require clearance from the BBBofC to make his comeback and remains the subject of a UK Anti-Doping investigation. "So a massive shout out to Wladimir Klitschko", said Joshua. "As I said, I'm not ideal but I'm trying and if you don't take part you're going to fail", said Joshua.
"I want to give 90,000 people another chance to come back and watch some boxing here". 19-0, three and a half years in the game.
"He's been very dominant". He took a loss against Tyson Fury.
"I thought he would not get up", Klitschko said. He came to show what he was about, that he still had it.
"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".
"Maybe against anyone else in the division he may have come out on top".
"I've got nothing but love and respect for anyone who steps inside the ring".
Speaking at a post-fight news conference, the 2012 Olympic champion conceded some fundamental lessons had been learned, while he enjoyed confirmation that he can maintain his thunderous power into the championship rounds.
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