The Spanish league has described the transfer sanctions handed to the two clubs as "disproportionate" and "excessive"
Both Madrid giants will be unable to register new players during the next two complete transfer windows as a consequence of breaches "relating to the international transfer and registration of players under the age of 18".
Earlier on Thursday, Madrid and Atletico protested their innocence and announced they will appeal against the punishments, with La Liga confirming it will stand by each team.
The league believes that the penalties imposed are "disproportionate" and represent "excessive punishment".
In an official statement, La Liga said: "Following the sanction of the Fifa Disciplinary Committee to Real Madrid CF and Club Atletico de Madrid, as a result of having infringed the rules on international transfers of minors, La Liga wishes to express that Spanish football through its clubs supports the policy of protecting minors and the concern for their development and for their training.
"Furthermore, it also proposed to the RFEF [Royal Spanish Football Federation] an adequate system of compensation for training clubs, perfectly compatible with the development of minors.
"The conduct of Real Madrid CF and Club Atletico de Madrid has been always in favour of the respect, the interest and the training of the child. This has been evident in the various meetings held in recent seasons with specialists from all the clubs from La Liga in this field.
"Therefore, at La Liga, we believe that the penalty imposed is disproportionate, out of place and is an excessive punishment for both clubs based on their behaviour and the circumstances of each case."
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Barcelona were hit with similar sanctions in April 2014 – eventually served in January 2015 and the subsequent close season following a failed appeals process – and La Liga believes Fifa laws in this area are contrary to European Union legislation and do not protect young players.
The statement added: "La Liga has conducted analysis on the adequacy of the rules of 'protection' under FIFA, as well as the different standards of the European Union, the Swiss state [FIFA is headquartered in Switzerland] and Spain.
"Based on this [La Liga] will denounce to the appropriate bodies the current part of the regulation for the transfer of players under age, which does not conform to the law of the protection of minors.
"After learning of the sanctions to FC Barcelona, Real Madrid CF and Club Atletico de Madrid, La Liga considers that the aforementioned law does not really protect the child."