The Italy defender was scathing in his assessment of referee Michael Oliver, who awarded a stoppage-time penalty and sent off goalkeeper Gianluigi Buffon for dissent as reigning champions Madrid advanced to the semi-finals 4-3 on aggregate despite Wednesday's 3-1 loss.
It was a night of drama at the Santiago Bernabeu, where Juve remarkably overturned a 3-0 first-leg deficit to leave the quarter-final tie poised for extra time.
However, Medhi Benatia's challenge on Lucas Vazquez saw Oliver point to the spot at the death as Buffon protested furiously before he was shown red in the Spanish capital – Wojciech Szczesny brought on for a penalty that was blasted past him by Cristiano Ronaldo.
Incensed by the decision, Chiellini referred to last season's controversial quarter-final between Madrid and Bayern, who lost 4-2 at the Bernabeu and 6-3 on aggregate after Ronaldo's extra-time winner came from an offside position, while Arturo Vidal was sent off.
"It shouldn't be surprising, Bayern Munich went through it last year and this was Juve's turn," Chiellini told Mediaset Premium.
"Between the first leg and this one, just about everything happened. It's laughable that the Italian refereeing designator said things are going well in the Champions League.
"Nobody thought we could turn it around, but we believed and it'll help us for the next Champions League campaigns. It'll be an objective for the future."
Juventus president Andrea Agnelli urged the introduction of VAR to the Champions League, but Chiellini felt that missed the point in this case.
"It wasn't an issue of VAR, because the referee still needs to have courage and a conscience," said the 33-year-old. "The referee must try to be less of a protagonist and give only clear-cut decisions.
"You could tell at the time it wasn't a penalty, but seeing the footage back it's just laughable. We must remember that we beat Real Madrid 3-0 on their own turf and only a crazy person would've believed that going in.
"We could've scored five or six goals, so we ought to be proud. We want to win the seventh Scudetto."
Chiellini was not alone in his criticism - Gianluigi Buffon also launched an astonishing broadside on the official.