The 39-year-old Povetkin, like Joshua an Olympic gold medallist, had previously lost only to Klitschko and over the distance when the great Ukrainian was at his peak.
Parker, of course, failed to build on the profile he received in the United Kingdom from their title fight by succumbing to a second successive unanimous points defeat to Dillian Whyte in August.
Warren insisted if Fury does pull off an upset over Wilder, Joshua will be unable to escape the pressure to square off against his long-time domestic rival.
Joshua's next fight will be on April 13 back at Wembley Stadium and while WBC title holder Deontay Wilder remains the favourite, a domestic dust-up with Tyson Fury or a re-match with Dillian Whyte are also on the cards.
"I think it's safe to say that team Joshua and Matchroom will never fight the gypsy king. If Fury beats Wilder, that fight against Joshua becomes even bigger than we're talking about". Very, very clear to see, avoid me at all costs.
"I believe Tyson Fury will be the victor of that fight so why on earth would anyone want to stand in its way?" added Warren.
Should AJ's next fight be against Fury?
It was a satisfying conclusion for WBA-IBF-WBO world heavyweight champion Joshua (22-0, 20 KOs), but he had some shaky moments early.
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Against Fury - or at least the version of Fury who took the three belts from Wladimir Klitschko which Joshua now holds - there could come a salutary boxing lesson. He's slow, methodical, ponderous at times.
Joshua's victory tees up a potential super showdown with Deontay Wilder next year.
Mike Costello, BBC Sport boxing correspondent: "It was a brilliantly placed and timed right hand. Good luck to both of them". We know the platform won't be built in one event, but it just delivered the biggest star in world of boxing... No-one wants to wait until December because it takes a long time to negotiate with Wilder's people.
He is already booked in to box again at Wembley on April 13, but the question of an opponent has still to be resolved. "Ask yourself why don't they want this?"
WBC titleholder Wilder (40-0, 39 KOs), 32, has signed to face Joshua's British rival Tyson Fury on December 1 at what is expected to be an American venue.
Joshua enjoyed a weight and height advantage going into the fight, not to mention a rowdy home crowd, and was the bookmakers' heavy favorite.
For Povetkin, this is likely to be his end at the top level and he gave it his all, wobbling Joshua on a few occasions early.