Joshua, who was knocked down in the sixth round, came back from the brink of defeat to stop Klitschko in the 11th and claim the biggest win of his career.
The fifth defeat of the Klitschko's career, and second in succession after losing to Tyson Fury in November 2015, could yet prove the last fight of a decorated career, but he will find Joshua a game opponent should he choose to fight on.
"I fought the better Wladimir Klitschko, not the complacent one, the guy who realised his mistakes and wanted to put it right," he said.
"Maybe against anyone else in the division he may have come out on top. I have the ultimate respect for what he's achieved inside and outside of the ring. I wouldn't mind fighting him again; if he wants a rematch no problem.
"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.
"(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."
The champion was then asked if victory, against one of the finest heavyweights in history and the 1996 Olympic champion, topped winning his gold medal at London 2012, and he responded: "No. It is what it is: there's one winner and one loser.
"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 want to catch up with family and go back to normal living."
Klitschko, 41, said he would take time to consider his future in boxing and exercising his rematch clause for a potential return, but that has no desire to fight on against any other opponent.
"I am not going to consider anything or be making any statements right now," he said. "It's too early; I actually feel pretty good, considering I lost. I will take my time. I have a rematch clause which I can execute at certain times, and right now will not be making any decisions.
"If I'm going to fight it'll be a rematch, of course."
He had blamed his unexpected defeat by Fury in November 2015 - his first for 11 years - on an "off-night", but eliminated that reason here.
"I thought he wouldn't get up (from the knockdown)," he said. "He managed to get up: respect. I felt he was out of gas and concentration. He recovered through the rounds.
"I could have done more to finish him off after he went down, but I was pretty sure 'This is going to be my night' so I took my time.
"How he's going to develop, we'll see. He's vulnerable, and this may be something he will need to work on, but he's today's success.
"I didn't have an off-night. I was in tremendous shape. All respect to Joshua."
Joshua's promoter Eddie Hearn revealed the heavyweight next plans to fight towards the year's end. He also claimed he had already received confirmation the defeat of Klitschko had broken British pay-per-view records, and that Joshua can only fight in similarly-sized venues hereafter.
"I don't think he'll box again until again between September and December," he said. "It's more likely to be (Cardiff's) Millennium Stadium if it's in the UK. We can't return to The 02, and Manchester Arena. That's what might take us to another territory (outside of the UK).
"The next phase is all about the big heavyweight championship fights."