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Atletico were defeated 1-0 by Real Madrid in their quarter-final second leg on Wednesday, as Javier Hernandez's late strike saw the holders through following a goalless first encounter.
That reverse effectively ended Atletico's hopes of claiming any further silverware this season, with Diego Simeone's side lying nine points behind leaders Barcelona in the league with six games to go.
The defending Liga champions occupy third - the final automatic Champions League qualification berth - and with a four-point gap to Valencia, Simeone's men still have plenty to play for in the remaining weeks of the campaign.
"We faced a great team that has a much bigger budget than us," defender Miranda said after the defeat to Real.
"They can hire many players and we tried, but unfortunately we conceded a goal with two minutes remaining.
"It was a difficult game. We were eliminated and now we have to lift our heads and think about the next game."
Atletico's recent domestic record is strong, with just one defeat in their past 14 outings, including four wins from their last five.
Visitors Elche have managed only seven more than that between them in 2014-15, Fran Escriba's side having toiled at the wrong end of the table for much of the campaign.
Atletico's only major injury concern surrounds Mario Suarez, who is struggling with a hamstring problem.
