Pique announced after the game that he plans to retire after the 2018 World Cup as a result of the criticism he has faced in Spain.
AS, among other prominent media outlets, ran a story -- which it later removed -- stating as fact that the Barcelona defender had cut his sleeves while questioning if there were anti-Spanish sentiments behind the move.
However, a statement from the Royal Spanish Football Federation clarified that both Pique and Real Madrid's Sergio Ramos had cut the sleeves of their long-sleeved shirts, which did not feature the same detail as the short-sleeved versions, to feel more comfortable.
The editor of AS, Alfredo Relano, on Monday said he was sorry for his newspaper running the story online and lauded Pique's contribution to Spain throughout the years.
"I offer Pique our apologies for the hastiness with which, for 20 minutes, this newspaper's online version initially reported on the storm whipped up on social media," Relano wrote.
"He has always been a model Spain player, like so many others from his club. Barcelona have contributed more men to the Spain team throughout their history than any other side, it should not be forgotten."
Relano even went on to urge Pique to reconsider his decision, just as Lionel Messi did earlier this year when he performed a U-turn after retiring from the Argentina national team.
Meanwhile, Pique's father has backed his son's move to call time on his Spain career.
"I tip my hat to what he has said," Joan Pique told reporters.
Prior to Sunday's controversy, Pique was accused of deliberately putting up his middle finger during the Spanish national anthem at Euro 2016, while he has regularly been jeered by Spain fans due to what some see as his anti-Real Madrid and pro-Catalan independence views.
"It's not because of what happened today," Pique said on Sunday when he communicated his decision to give up playing for Spain in two years. "It's because I always give my best on the field and, although there are some people who have thanked me, some don't think it's OK for me to be here."
Former Spain coach Javier Clemente has defended Pique for his retirement decision and praised him for his "sincerity."