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.
Striker Antoine Griezmann has encapsulated their impressive form, the France international netting six goals in his last four league games to take his tally to 20 in his debut season at Vicente Calderon.
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.
However, back-to-back victories over Cordoba and Real Sociedad have lifted them to 14th, six points clear of the drop zone.
The strugglers suffered a blow this week with the news that Jose Angel Alonso has suffered a torn anterior cruciate ligament in his left knee.
The defender has made 13 league appearances this season, but is now expected to be out for around six months, with surgery scheduled for mid-May.
Atletico's only major injury concern surrounds Mario Suarez, who is struggling with a hamstring problem.
In their three meetings with Atletico since gaining promotion to La Liga at the end of 2012-13, Elche have lost 2-0 on each occasion.
They have their work cut out to amend that record against a side that has lost only once at home in the league since May 2013.
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