The Spanish club said in a statement that several refereeing decisions across both legs of the tie, which Atletico won 3-2 on aggregate, "did not comply with the Laws of the Game, resulting from an incorrect application of the regulations and a lack of appropriate intervention by the VAR system in incidents of clear significance."
The Catalan club, which finished both matches with 10 men after the dismissals of Pau Cubarsi and then Eric Garcia, believe they were on the wrong end of several contentious decisions, including two potential penalty situations that did not trigger VAR intervention.
"The accumulation of these errors had a direct impact on the course of the matches and on the final outcome of the tie, causing significant sporting and financial harm to the club," the reigning Spanish champions added.
Barcelona said the club "reiterates the requests previously made to UEFA" and offer to "collaborate with the organisation with the aim of improving the refereeing system to ensure a more rigorous, fair and transparent application" of the regulations.
On Tuesday, UEFA had rejected as "inadmissible" the five-time Champions League winners' initial complaint regarding a handball on a goal kick by Atletico defender Marc Pubill in the first leg, which his side won 2-0.