Thomas Cook and easyJet, which both offer UK residents holidays to the hotel in the resort of Protaras, said last night they were "extremely concerned" by the allegations.
Antonis Alkiviades, who works at MedVets, the surgery which cared for Billy, said: "When we went to the hotel, he was already in a coma. We were shocked and it was even more of a shock when we were told he was put into this bin."
Mr Alkiviades said Billy had a broken back and other broken bones and was unable to breathe. Vets later realised he had brain damage.
Billy was visited by dozens of concerned locals and tourists. Briton Lynn Gandy, 61, said: "He looked terrible. He was a poor, frail, little dog. To think somebody could throw a live animal into a crusher beggars belief. It is savagery."
Another woman said the local reaction to Billy's death had been so fierce that she feared there would be riots. On Friday, British tourists joined expats marching outside the Anastasia, which is part of the Tsokkos group, Cyprus's largest hotel chain.
They held banners with slogans reading 'Punish people who abuse animals' and 'Support Billy's Law and stop animal cruelty now' while also chanting "Justice for Billy".
Ross Breakwell, from London, who was on holiday in Cyprus, said: "I never imagined a country within the European Union could be so lax when it comes to something as important as animal rights.
"I'm shocked and disgusted by this incident. It will make me think twice before coming back to Cyprus and I definitely would never stay in a Tsokkos hotel. All tourists to Cyprus should boycott the company."
Mr Alkiviades also called for tougher laws on the island. He said: "You have the RSPCA in the UK. We don't. We need people to be able to reinforce laws and punish cruelty."
Nicos Anastasiades, the president of Cyprus, condemned Billy's death and described the incident as "a disgrace for society and our country".
Thomas Cook said: "We take such incidents extremely seriously, and in no way condone this type of alleged behaviour. This is obviously a very serious allegation, given that Thomas Cook closely audits properties to ensure the very highest levels of health, safety and quality standards are maintained."
Tsokkos Hotels said: "Hotel management received complaints from customers about the fact that a sick stray puppy wandered around. The hotel manager immediately gave instructions to two employees to take the puppy to a local shelter to obtain appropriate care.
"Unfortunately, the employees did not follow the instructions and proceeded to an inhuman act, unacceptable and condemnable by Tsokkos Hotels. As soon as Tsokkos Hotels became aware of the incident, the puppy was transferred to a veterinary clinic to receive all necessary treatment."
- Mail On Sunday