But Poyet told BBC Sussex: "We don't agree with players agreeing contracts and not signing them.
"Six months ago nobody knew him. Now he's in the spotlight because of Brighton. The offer is gone and now he is not going to be our player."
Poyet added: "He decided to wait for the possible offer of another club in this division who we can't compete with.
"If somebody thinks we are the Chelsea or Manchester United of the division we are not.
"I was expecting a bit of something back. I couldn't get it. We agreed it and he didn't want to sign it.
"I want to thank him for his services because he helped us a lot and I think people got really close to his qualities."
Right-back Calderon has made 20 appearances for the Seagulls since signing on a free transfer in January but missed Albion's last three games of the campaign with a hip injury.
Source: BBC Sport
Source: BBC Sport