The Catalan club finished bottom of the table, with just 25 points from their 38 games, and lost their top-flight status for the first time since the early 1990s.
But Espanyol now say they were unable to compete effectively after lockdown due to a number of circumstances.
In a long statement posted on Monday, the Pericos claimed they had been particularly affected by the exclusion of fans after the restart, and added that they found it difficult after a number of their players tested positive for Covid-19 during the break.
"The absence of fans in the stadiums was a great detriment to all the clubs, but in our case, that circumstance has been much more harmful since we were playing against five direct rivals in the fight for survival," the club said.
And on the effects of the positive tests, they added: "Clubs like Valencia CF and ourselves made an effort to compete normally, despite having confirmed that, in the professional squads, during the months of March and April, there were a good number of players infected by Covid-19, with the consequent affectations that the disease leaves for many weeks."
Espanyol returned to action in June with a win over Alaves and a draw against Getafe, but the Catalans lost their next eight league games and finished 12 points behind 17th-placed Celta Vigo.
Pointing to those circumstances and the financial insecurity post-pandemic, Espanyol went on to call for "the elimination of relegation across LaLiga (which incorporates both LaLiga and Segunda), in the same way that happened in [the competitions] organised by the RFEF."
Espanyol's women escaped relegation after La Liga Iberdrola was suspended in May, with the Catalans rock bottom on five points and without a win from their 21 fixtures played.