The Jet Airways representative says the airline has embarked on a global review of other airport and airline procedures.
The representative said: "We sincerely regret the accidental demise of James Dean, pet cat of Ms. Preeti Varma. All our staff are fully conversant and trained in the process of handling household pets and necessary infrastructure is available at the airports to deal with such movements of pets.
"If the actions of any members of our team came across as insensitive we would like to assure that this was unintentional and to apologize to Ms. Varma."
International Pet Travel Consultant Anupama Vinayak, who runs pet relocation service Furry Flyers in India, which flies 40-50 pets in and out of India each month, said she had never heard of an incident like this.
But she added: "Pet travel is still in a very nascent stage in India. Airlines are trying to put their best foot forward but there still is a lot of room for improvement because India itself is not a very pet-friendly country," she said.