After the national team's victories at the last two European Championships and the 2010 World Cup, the country is high on confidence and wants an Olympic gold so Spain can hold all three titles at once. But Milla is discouraging the hype.
"The national team is one team and the Olympic one is another. I don't like to speak of favourites," Milla said Wednesday, adding that Brazil and host nation Britain shouldn't be overlooked.
Spain faces Japan in the tournament opener Thursday at Hampden Park, and that's the only thing Milla wants his players to focus on.
"Since we started our preparations, we only have been thinking about the first match, in respecting our rival," he said. "It's a difficult clash and we have to be at 100 per cent. Japan will be a very difficult rival."
But Spain might be without one of its most creative players for the match. Forward Iker Muniain, doubtful because of a right leg injury, will undergo a test to determine if he will be ready. The rest of Spain's players are fit.
"The signals we are getting are good, but he has been sidelined for a week without training alongside his teammates," Milla said. "We'll see tomorrow how he is and how the test goes."
With two of world football's most important trophies already in their hands, there has been concern that the Spaniards might view the Olympic tournament with apathy since some critics view it as a lowly and unimportant competition.
Captain Javi Martinez doesn't see it that way. Martinez, Juan Mata and Jordi Alba are all on the Olympic squad after being part of the victorious Euro 2012 team.
"For the three of us who were at the European Championship, we are approaching it (the Olympics) in the same way," Martinez said. "It's an opportunity to keep growing and to continue on Spain's victorious path."
Martinez has also stressed the importance of getting off to a winning start against Japan.
"To have a good tournament, it's necessary to start well. They are three important points in the group stage," Martinez said, adding that a victory would give the team "confidence and tranquility" for its remaining two matches.
The Spaniards' other Group D opponents are Honduras, who they play in Newcastle on July 29, and Morocco, who they face in Manchester on Aug. 1.
The rainy weather in Scotland has also led to concerns that a soggy pitch at Hampden Park could hinder Spain's slick passing game.
"The issue of the field is one of equilibrium," Milla said. "If it rains, the pitches here fare well since it rains so much here. If there isn't too much water and it's not dry, it's perfect. But those would be good circumstances for Japan too, because they are quick and they play well in those conditions."