The 41-year-old Ukrainian fought back from a fifth-round knockdown and seemed on the brink of victory when he dropped Joshua in the sixth, but the British heavyweight bounced back to send his opponent to the canvas twice in the penultimate round.
In the aftermath of an epic fight, Klitschko confirmed a rematch clause, and would welcome a second chance to regain the IBF and WBA 'super' titles which are currently held by Joshua.
"Of course, we have it in the contract, I'm right now interested," Klitschko told Sky Sports News. "Analyse what the heck has happened.
"Congratulations to Anthony, he got up, he fought back, and he won the titles. 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.
"I love you too guys (the crowd). I hope you enjoyed the fight. 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. A lot of respect to you guys, 90,000 people present, you were awesome guys. Thank you so much for your support to the sport and this fight."