The Spanish Football Association has sent a letter to its English counterparts apologising for racist chanting during Wednesday's match.
The Spanish FA also apologised for similar incidents during Tuesday's Under-21 international.
"The FA welcomes the response and now looks forward to receiving details from Fifa on its investigation initiated on Thursday," said an FA statement.
The FA is awaiting Fifa's reply after sending them a dossier on the abuse.
The apology, written by general secretary Jorge P Arias, was in reply to a letter sent by the English FA.
However, the dossier sent to Fifa by the English FA highlights its concern at the lack of action so far taken against Spain manager Luis Aragones for his pre-match inflammatory remarks.
And if racism is proved, the Spanish FA could face a large fine or Spain could be forced to play games behind closed doors.
The FA's head of media Adrian Bevington said that had the incidents occured in England, the technology is in place to ensure most of the culprits would be caught.
"If that had happened in an English stadium, I'd hope those responsible could
be identified through the use of CCTV footage and then be punished and prevented
from attending future matches," said Bevington.
"As we found and learned, the key thing along with any penalty is that
education and campaigning is the way forward too."
A Fifa statement on Thursday said: "We are concerned about the latest surge of racism and harshly condemn this. (Fifa) will demand explanations from the Spanish Football Association."
Fifa president Sepp Blatter said there was, "no room whatsoever for racism or discrimination in our sport".
He added: "The world is already too full of conflict that has its roots in racism and discrimination. Football has a positive influence."
Early on Friday, Spanish foreign minister Miguel Angel Moratinos apologised "in the name of the Spanish government to anyone who may have felt offended by these expressions".
"I have had the opportunity to comment and discuss it with my (British) counterpart Jack Straw and I again express that Spain is a country of tolerance where expressions of racism should have no place," Moratinos said.
Sports minister Richard Caborn said: "I will write to my Spanish counterpart to express my outrage. I would like the Spanish FA to condemn the scenes.
"I also expect Fifa and Uefa to fully investigate the issue.
"There is no place for racism in football or modern society, and I strongly believe that action needs to be taken at the highest level."