Joshua shared a dramatic fight with Klitschko at Wembley in April, which saw him climb off the canvas to produce a stunning 11th-round stoppage victory.
Fury criticised Joshua's performance in comparison to his own points win over Klitschko, branding the 27-year-old as a 'pumped up weight-lifter', but the WBA 'super' and IBF title holder has issued a dismissive response.
He just walked around the ring for like 12 rounds, it's boring. It's not winning, it's how you win.
Anthony Joshua on Tyson Fury
"He didn't throw a punch. He didn't come to fight," Joshua exclusively told Sky Sports.
"He just walked around the ring for like 12 rounds, it's boring. It's not winning, it's how you win.
"His stock didn't rise. Your stock has got to rise and he could have had the better win, but when people look at it, many years after, ask them whose fight they will remember."
Joshua believes 'the public want to see' a fight with Fury, but refused to speculate about whether the former world champion will employ more aggressive tactics in a British battle.
"Ask his trainer, I don't know how he will try to beat me," said Joshua.
Fury's return to boxing has been put on hold until the outcome of a UKAD hearing that is yet to reach a final ruling on his suspended drugs ban, but the 28-year-old welcomed Joshua's verbal challenge.
"Let me get my situation on track, get fit and then I'll fight you. May the best man win," he said in a video posted on Instagram.