Pique, who has been booed by Spain supporters in the last year, caused a stir on social media by appearing against Albania with the sleeves cut off his Spain shirt, thus appearing to remove the bands displaying the red and yellow colours of Spain.
The RFEF released a statement on Monday with a photo highlighting that the long-sleeved shirt Pique had modified did not have the red and yellow stripes on its original design.
"The Royal Spanish Football Federation wishes to show its support to the international footballer Gerard Pique about the controversy regarding the cut made on his jersey in the match against Albania," the statement said.
"This is contrary to some malicious comments made after the Spanish player was accused of cutting the sleeves of the jersey to avoid wearing the band with the national colours.
"The RFEF wishes to explain that said band on the Adidas jersey only exists in the short sleeve version, and not on the long sleeve, which is the one Pique used in the match.
"Gerard Pique cut the sleeve with the sole aim of playing more comfortably, the same way other players have done on many occasions."
Spain coach Lopetegui meanwhile said he sympathised with the defender.
"This does deserve any comment as I don't think it's a serious issue. I also understand Pique. We are very happy with his performance and of the rest of the team," Lopetegui told Teledeporte.
"We're calm and relaxed about this. Some journalists might find this interesting but us professionals do not. Pique's commitment cannot be doubted. We're going to let this issue calm down, there's no need to jump to conclusions."
(Editing by John O'Brien)
