Cleverly lost his WBO light-heavyweight title in Cardiff on Saturday night as powerful Russian Kovalev took advantage of the Welshman's careless tactics to floor the champion twice before forcing the stoppage.
Cleverly was never really in the fight, allowing Kovalev to land his heavy blows almost at will while firing back very little in return. He went down twice in the third round and was out on his feet when the session ended, before Kovalev pounced in the fourth, prompting referee Terry O'Connor to stop the contest.
While Kovalev's win was one-sided, Cleverly may be intelligent enough to learn from the defeat and make a better case next time. Warren, however, confirmed there was no rematch clause in the fight contract and was wary of demanding a shot at redemption for his 26-year-old fighter.
"We'll see what happens with regards to any rematch," Warren said.
"It's early days. We'll let him have a break. It's all a bit raw at the moment so we'll have a chat in a few weeks and see where we go."
He added: "There isn't a rematch clause but I'm sure we could talk.
"At this stage I'm not even thinking about a rematch. The most important thing now is for him to go and have a holiday and when he comes back we'll chat and see what is the way forward."
Cleverly, who declined to speak to reporters after the fight, had actually chosen Kovalev as his opponent for the voluntary defence.
Warren insists the Cefn Fforest boxer, whose record now reads 26-1 (12KOs) did not underestimate the powerful Russian (22-0-1, 20KOs).
"It was high risk and I really did think he could win it," he said.
"He asked for the fight. We met in London a few months ago and he actually said that was the one he wanted.
"He absolutely respected Kovalev's punching power. We all knew he could punch but he's one of those fighters that anybody who uses their brain and boxes will beat. Of course he can punch. There are lots of guys out there with serious knockout power in either hand.
"Nathan just couldn't get going. There was a period when he caught Kovalev with some nice jabs and the guy definitely didn't like it. But once he got clipped he never got over it."
Warren added: "It's time to go back to the drawing board.
"He's only 26 years of age and it's not the end of the world. Worse fighters than Nathan have lost and come back and there's no reason why he shouldn't do. But he's got to learn from it and we'll see where we go from there.
"He's going away to Cyprus for a couple of weeks and when he comes back we'll sit down and work out a gameplan."
Exultant Kovalev admitted Cleverly presented less of a challenge than he expected.
"It wasn't easy, because Cleverly was the champion," the Florida-based Russian said. "But he was a 'local' champion. To be honest though, I've had harder fights in my career. I was ready for a hard fight.
"A rematch? Why not. But it's a question for my promoters, not me."