Chelsea signed the Argentina international on transfer deadline day from Benfica after meeting the midfielder's €121 million release clause.
"We lost a great player but I'm not going to cry for a player who doesn't want to represent Benfica," Rui Costa told BTV as reported in Record.
"[I] don't cry for players who don't want to be here. I was raised in this club and told to honour the jersey, otherwise where is the phrase 'we only want players who honour the jersey'?"
A World Cup winner with Argentina, Fernandez, 22, had only joined Benfica from River Plate in July in a €14m transfer.
Rui Costa was reluctant to transfer Fernandez midway through the season and remained hopeful that a deal could be reached for the midfielder to continue at the club until June.
"At lunchtime [on Jan. 31], I put on the table the proposal that Chelsea buys [him] now and takes him only in the summer," Rui Costa said.
"We tried to explain to him, he's an extraordinary player. Would he lose value if he stayed at Benfica until the end of the season? Not at all. Many 'Chelseas' would appear. I don't have the slightest doubt. But I also understand that the player wants to settle immediately, afraid of losing an offer that he would consider huge.
"I respect the fear of losing a big contract, it's another thing for him not to lose a euro and still not want to stay. And this is where I move.
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"He showed no commitment to Benfica. Here I thought he couldn't play for Benfica anymore. As a fan, I didn't want this player anymore, as a manager it wasn't a solution either and he couldn't enter the locker room again. That's when I made the decision to let him go."
Rui Costa added his club offered Fernandez an improved wage package to try to convince him to stay.
"The salary increase was discussed, the proposal was made," he said. "But [to pay] half of Chelsea's salary proposal was unfeasible for us.
"We never managed to get through to him to convince him. Whenever Chelsea approached the value of the clause, there was virtually no chance to alter his mind. He was very incisive in wanting to leave Benfica."
Rui Costa, nevertheless, said he respects Fernandez's decision.
"I'm sad that he left but I have a clear conscience that I did the best for Benfica," he said. "Enzo was treated well by everyone from the moment he arrived until he left.
"I had hoped that it would give Enzo pleasure to fight for the title. When it became very clear that he wasn't committed, I didn't want him to wear the Benfica shirt anymore. We want a team committed to the fans. I respect his decision, though."
Fernandez, who signed a contract with the Premier League club until June 2031, said it was "a dream come true" to join Chelsea.