Klitschko became the first man ever to knock Joshua down in a professional fight with a stunning sixth-round salvo.
But the Brit got up off the canvas to record a knockout in the 11th round and seize two more world championship belts to add to his IBF heavyweight title.
Klitschko, 41, had been expected to retire after the defeat but instead he suggested in his parting Tweet from London that he would fight again.
“Leaving [London] with a feeling everyone won on Saturday night: the sport, the fans and even I on respect,” Klitschko said.
“Cheers and I’ll be back!”
It reinforces the claim the Ukrainian made in the ring immediately after his defeat that a rematch clause exists between himself and Joshua.
“Of course, we have it in the contract, I’m right now interested,” Klitschko told Sky Sports.
“Analyse what the heck has happened.
“I did enjoy the night as well as you.
“I wish I would [have] raised my hand instead of being someone that didn’t make it and win the titles back.
“But congratulations to Anthony, he got up, he fought back, and he won the titles.
“Both fighters were really giving their best.
“The best man won tonight and it’s an amazing event for boxing.
“Two gentlemen fought each other.
“I say gentlemen, because boxing came from England.
“Anthony was better today than I.
“It’s really sad that I didn’t make it tonight.
“I was planning to do it – it didn’t work – but all the respect to Anthony, congratulations.”
If Joshua does not fight Klitschko, Hungarian heavyweight Kubrat Pulev is favourite to challenge for the titles next.
The 35-year-old has lost just once in his 26 fights with his one defeat coming against Klitschko back in 2014.
