Castro said Vitolo had in principle agreed to renew his contract with Sevilla before paying his own release fee of 37.5 million euros and agreeing to join Las Palmas until January and then Atletico.
"Sevilla will do everything possible to defend their interests without sparing absolutely anything," Castro told Sevilla's Radio Station.
"The only thing I can say is that the club made a tremendous effort so their captain could stay here and he has not been true to his word, he lacked respect for Sevilla and their fans. He has let us down as a person."
Vitolo appeared at La Liga's offices on Wednesday to pay his release fee, which enabled him to sign for former side Las Palmas, where he will remain until he can join Atletico.
"We are disappointed with the attitude of the third parties,(Atletico and Las Palmas)," added Castro. "This has deteriorated relationships with these clubs that were marketing our player."
Spain international Vitolo, 27, has agreed a contract with Atletico until 2022.
"Vitolo is a player with extensive experience and quality, who has played for Spain 11 times and become one of the most dangerous players in La Liga in recent seasons," Atletico said in a statement.
(Reporting by Rik Sharma, editing by Ed Osmond)
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