Spain failed to even score a goal in their three matches at the Games as they lost 1-0 to Japan and Honduras before finishing with a 0-0 draw against Morocco.
Milla had guided Spain to the European Under-21 Championship title last year and appeared well positioned to lead them to a defence of their crown in Israel next summer as they currently top their qualifying group with just two games remaining, but his position will now be taken up by former under-19 coach Julen Lopetegui.
Montoya believes it is unfair for Milla to take all the criticism for the team's failure at the Olympics.
He told AS: "The fault for the sacking is the players' because we didn't play well and we don't feel good about this. During the tournament we didn't have much luck in front of the opponent's goal and we gave away quick goals.
"Now we have to work to qualify for the Euros in Israel but I don't think Milla will find it difficult to get a club job because he is a great coach."
Villarreal goalkeeper Diego Marino echoed Montoya's sentiments and hinted that he believes the decision to remove Milla was an over-reaction on the part of the Spanish Football Federation.
He said: "It was a sacking that I didn't expect, we have only two games to qualify for the Euros and I thought he would continue.
"It is a decision that the federation have taken and it is because they think it is for the best.
"The results were due to a little bit of everything. We weren't as prepared as we thought or the other teams were much better prepared than us.
"In the first game we weren't good, but in the other two we deserved better luck, we just didn't get it."
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