Fury returned to the ring for the first time since his thrilling draw with Wilder in December and he made light work of the previously unbeaten Schwarz in Las Vegas.
After the victory, Fury said he intended to fight once more before seeking a rematch with WBC title-holder Wilder.
Yet Wilder, who, like Fury, is still yet to taste defeat, was less than impressed by his display on Saturday given who he defeated.
"It was a cool performance; It wasn't much of an opponent," Wilder told The Athletic.
I Live in America! pic.twitter.com/DR1ZOa1RBg
— TYSON FURY (@Tyson_Fury) June 16, 2019
"I think [Schwarz] only threw four punches. He was a punching bag.
"Fury did what he was supposed to. They're trying to promote him up, saying things, selling this story about him over and over again, talking about him as the lineal champion... it's building him up. But the performance was just okay."
Though his time in the ring was short, Fury earned plaudits for his impressive nous, at one point eluding some wild Schwarz shots with evasive head movement.
Yet Wilder thinks the Fury he faced, and knocked down twice in the ninth and 12th rounds, was the best version he will ever be.
"He was a better Fury against me, in A-plus, tip-top shape," Wilder added.
"That was the best Fury you'll ever see in his career."
Photo Getty Images. Caption: Deontay Wilder and Tyson Fury