The Spanish were widely considered favourites for the title, but crashed out in the group stages following consecutive 1-0 defeats to Japan and Honduras.
And Mata, who was one of Spain's three picks over the age of 23 for the Games, took to Twitter to express his belief that Spain had been undeservedly knocked out of London 2012.
He wrote: “Thanks for your support! It's been a pity, I do believe that this team deserved more... We have to learn and grow from defeats."
The Chelsea midfielder, who was part of Spain's victorious Euro 2012 squad this summer, also called for his team-mates to put in a professional performance in their last Group D game against Morocco on Wednesday.
He added: "Now we have to stand up and play the last match with professionalism. Hugs!”