The final in Paris was delayed by 36 minutes after thousands of Liverpool supporters were unable to get into the Stade de France for the match on May 28, which Real Madrid won 1-0.
French police were filmed using tear gas on fans, including women and children. Although UEFA initially blamed the Merseyside club's fans for the mayhem, the governing body later apologised following the release of an independent review.
On Tuesday, UEFA said it would refund Liverpool fans who attended last year's final in Paris and that the English club had confirmed it would implement the refund scheme, which would cover all of the club's ticket allocation for the final.
UEFA said Real Madrid fans and neutral supporters who met the refund criteria would be processed via its customer service.
Tickets for the final cost between 62 pounds ($74) to 610 pounds ($733).
"Real Madrid has been holding talks with UEFA with the aim of assessing the compensation that will be offered to the fans," Madrid said in a statement.
"Our club was entirely confident that these solutions would be in line with the seriousness of the events, the extent of the damage caused and UEFA's responsibility for them.
"Regrettably, our club believes that UEFA's proposal ... is insufficient. It merely consists of the reimbursement of the ticket price, which is also subject to the fulfilment of a series of requirements, including providing proof of the time of access to the stadium."
Madrid added that an online assistance service would be set up for fans to make "appropriate claims" against UEFA.
"... All the fans experienced an unacceptable delay at the start of the match. In addition, there was unacceptable insecurity both in accessing and leaving the stadium, as well as additional harm such as theft, assaults and threats," Madrid said.
"For this reason, Real Madrid has decided not to cooperate in the restricted compensation procedure proposed by UEFA, which we ask to redress the situation and assume its full responsibility."
UEFA said later on Thursday that its refund scheme had been devised following "wide consultation", adding that Madrid was "the only party which did not cooperate with the Independent Review".
"Despite several requests made by UEFA, Real Madrid declined to contribute to the planning of the refund scheme and finally declined the invitation to process refunds to entitled people who bought their tickets from the club," UEFA said.
"The special refund scheme is for fans most affected when accessing the Stade de France ... regardless of the team they support... UEFA continues to believe the scheme is fair and accurately reflects the relative problems faced by fans on the night."
