The Ukrainian suffered the fifth defeat of his decorated career, and the second in succession, when he was dramatically stopped in the 11th round of a thrilling clash at Wembley Stadium by IBF and WBA heavyweight champion Joshua.
Klitschko had looked on the verge of victory when he heavily dropped Joshua in the sixth round, after which he felt he could have done more to finish the younger fighter off.
Even at 41 years old, Klitschko proved he remains among the world's leading heavyweights, and insisted he would explore his rematch clause for a potential return.
"I am not going to consider anything or be making any statements right now," Klitschko said.
"It's too early; I actually feel pretty good, considering I lost. I will take my time. I have a rematch clause in the contract, 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."
The Ukrainian, who has secured 54 stoppages from his 63 victories, spoke of his surprise that Joshua succeeded in recovering from such a heavy knockdown.
He also insisted that the 27-year-old champion remains "vulnerable" before, having long dismissed his points defeat by Tyson Fury in 2015 as an "off-night", saying he had no excuse this time around.
"I thought he wouldn't get up," Klitschko said. "He managed to get up: respect. From that moment 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.
"I got caught and the blood was streaming into my eye, and it was difficult to see due to the thickness of the blood. I recovered well, took a beating, but recovered well.
"I've always been a fan of AJ's talent since our sparring sessions. 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.
"He's the unified champion, so you have to respect it. It was a good fight. The fans enjoyed it. I wish I'd been the winner.
"AJ did a good job. He was trying, was focused, and even if he went down, he got up, came back. He managed to see my left hook and block it, so he was well prepared.
"I didn't have an off-night. I was in tremendous shape. All respect to Joshua."
Klitschko was also asked about the video prediction he had recorded onto a memory stick and which he plans to auction, and he responded: "The prediction is right there.
"Only the buyer of the robe: it doesn't really matter. I'm sure there's going to be a person who'll buy it. If they decide to share it with us, he or she is welcome, but my prediction is right there.
"We both did great, we did a lot for the sport how we promoted this fight, respectfully treated each other. On the response from the fans, it was a great night. It was an exciting, exciting fight: I'm happy."