After suffering a shock defeat by Japan in their 2012 Olympics Group D opener, La Roja needed to get something out of the game in Newcastle, but they succumbed to an early goal from Jerry Bengtson.
Spain created numerous chances, hitting the woodwork three times in total as well as having a strong spot-kick shout when Adrian was bundled over in the area by Arnold Peralta.
"The referee did not want to talk about it," Milla told reporters after the game. "But I had the feeling that there was a penalty."
Milla therefore felt that Spain's obvious sense of frustration, which manifested itself in seven bookings and an outbreak of in-fighting, was somewhat understandable.
"It was an intense match and there were disputes between the players and that can happen," he reasoned. "When you are playing at such intensity yellow cards can happen.
"As you can imagine everybody is down and disappointed. We played well and we put on a good show. The only thing missing was the goal and we deserved to win, but now we have to analyse what happened.
"But we will keep believing in the way we play. We will keep pushing our football philosophy because all that was lacking was the goal. We played some great stuff."
Spain, who had been one of the pre-tournament favourites, sit bottom of their group with zero points, meaning they will have nothing but pride to play for in their final group game against third-placed Morocco.