"What can I say? 19-0, three and a half years in the game. As I said, I'm not perfect but I'm trying and if you don't take part you're going to fail," said Joshua who was put on the canvas for the first time in his career in the sixth round of the see-saw battle.
A round earlier Klitschko was floored but the 41-year-old Ukrainian rose to launch attacks that brought him back into contest.
"As boxing states, you leave your ego at the door and you respect your opponent. So a massive shout out to Wladimir Klitschko," said Joshua.
A third defence of his IBF world heavyweight title also earned Joshua the vacant WBA belt as he became the first British heavyweight since Lewis in 2002 to hold two versions of the world title.
It was Klitschko's first stoppage defeat since Lamon Brewster beat him in 2004 and leaves his record at 64 wins and five defeats. "The best man won and it's a massive event for boxing," Klitschko told Sky Sports.
"Two gentleman fought each other. Anthony was better. It's really sad I didn't make it."
Klitschko was trying to reclaim two of the three belts he lost to Joshua's fellow Briton Tyson Fury by an upset on points in November 2015. He had not fought since then and entered the ring as the underdog.
The Briton left Klitschko wobbling in the fifth round with a left hook before landing a series of blows, including a right uppercut, which sent the Ukrainian to the canvas.
Klitschko got up and in the next round Joshua was felled by a right hand to the temple.
He was up after eight of the 10 seconds allowed before being deemed knocked out and survived the round.
In the 11th Joshua unleashed a right uppercut to snap back Klitschko's head, followed by another right to send his opponent to the canvas. Klitschko got up but was nailed by a series of punches from the right giving referee David Fields no other chance but to stop the fight.
“I don’t mind fighting him again if he wants the rematch," Joshua said at a press conference after the fight. Big respect to Wladimir for challenging the young lions of the division.”
Klitschko refused to make any commitment on his future and whether he would retire after a second successive defeat. "I'm not going to make any statements. I will take my time and let you know," Klitschko said. "I have a rematch clause in the contract which I can execute. I don't feel like someone who lost. Even though I didn't get the belts, I definitely gained although I lost."