Rubiales is suspended from all football-related activity for 90 days by FIFA as the governing body carries out an investigation into his nonconsensual kiss of Jenni Hermoso during the medal ceremony.
"The players of the men's national team would like to highlight several issues regarding recent events that have damaged the image of Spanish football," said Morata, seated alongside fellow captains César Azpilicueta, Rodri and Marco Asensio.
"Firstly, we would like to once again express our pride and our most sincere congratulations to the women's national team for winning the World Cup. It is a historic milestone full of meaning that will mark a before and after in Spanish women's football.
"For this reason, we would like to express our regret and solidarity with the players who have seen their success tarnished.
"We also wish to reject what we consider to be unacceptable behaviour on the part of Mr. Rubiales, who has failed to live up to the institution he represents.
"We stand firmly and clearly on the side of the values that sport represents. Spanish football must be an engine of respect, inspiration, inclusion and diversity and must set an example with its conduct both on and off the pitch."
Morata finished by asking for the players to now be allowed to focus on "sporting issues" as they prepare for Euro 2024 qualifiers against Georgia and Cyprus.
The incident with Hermoso has garnered most of the attention since the final, but Rubiales has also been condemned for grabbing his crotch, hugging and kissing other players and carrying another over his shoulder.
In addition to FIFA's investigation, the Spanish government's Supreme Sports Council (CSD) is also seeking his suspension, although it encountered a setback in its attempts to do so from Spain's Administrative Sports Court (TAD) last week.
The TAD opened a case against Rubiales but classified his infraction as "serious" rather than "very serious," which prevents the CSD from stepping in and suspending him in parallel to FIFA's ban.
However, the CSD has still requested the TAD suspend him as it carries out its investigation, which could end with a ban of as long as two years.
Spanish prosecutors have also opened a preliminary sex abuse investigation into Rubiales, although any action would be subject to Hermoso pressing charges.
In the meantime, the RFEF, led by acting president Pedro Rocha, joined calls for Rubiales to step down last week. But Rubiales still refuses to resign and, in a statement released Friday, pledged to keep fighting to clear his name.
"I will continue to defend myself to prove the truth," he said, criticising the "unprecedented political and media lynching" he has faced.