"It's a total lack of respect for his teammates and the club," said an angry Del Nido in an interview with Cadena Ser.
Del Nido added that Alves's position was outrageous given the current difficult times at Sevilla, whose defender Antonio Puerta is in intensive care in hospital after suffering two heart-attacks during Sunday's 4-1 victory over Getafe in the opening round of the Spanish Primera League.
Alves, who has also generated interest from Spanish giants Real Madrid and Barcelona, did not play in the match against Getafe due to a muscular problem.
The Brazilian's hopes of a move to Chelsea were dashed when the London club refused to meet Sevilla's $54.6 million asking price and opted to sign compatriot Juliano Belletti from Barcelona for $7.5 million instead.
Sevilla are the reigning Uefa Cup champions, and defeated Real Madrid 6-3 on aggregate in the pre-season Spanish Super Cup.
Puerta still critical
Meanwhile, defender Puerta remains in a critical condition after collapsing and losing consciousness during Saturday's match, and is in intensive care "with assisted ventilation and under sedation after a prolonged cardiac arrest," doctors at the Virgen del Rocio hospital in Seville told a news conference on Monday.
"The arrest has been caused by repeated incidents of serious ventricular arrhythmia. These are being controlled with treatment.
"The patient's situation, 36 hours after being brought in, continues to be critical as a result of the serious consequences of the cardiac arrest, including some effects on the brain.
"When a patient is in a critical state there is always a risk. Also, after a cardiac arrest as prolonged as this it is too early to give a prognosis or to venture possible after-effects."
Puerta, a 22-year-old Spanish international, collapsed in the 35th of the match against Getafe after jogging back towards his own goal at the Sanchez Pizjuan.
Team mates and medical staff rushed to his side and were seen preventing him from swallowing his tongue as he lost consciousness.
The defender was able to walk from the pitch, but doctors said that he collapsed again in the dressing rooms and had to be given cardiac resuscitation before being taken to hospital.