Emma McNulty said the death of 14-year-old terrier, Millie left her physically sick with grief and unable to attend work.
The 18-year-old from Glasgow said her employers, a sandwich shop, told her to find cover for her shift or risk dismissal.
She claims that after she was unable to find someone to replace her, her employment was terminated.
Now, the student has launched a petition urging employers to recognise the emotional toll of losing a pet and ensure staff are given time to grieve.
Since uploading the petition to change.org on Tuesday, it has already attracted more than 3,000 signatures of support.
Ms McNulty said Millie was a “valued” member of her family and a companion, with whom she had a close relationship.
However, she unexpectedly took ill one Saturday evening, and had to be put to sleep the following day, a turn of events that left the teenager reeling.
She explained: “I informed my manager I could not come into work as I was too devastated and physically sick to do so.
“Instead of being shown the compassion and sympathy stated in the contract, I was sent a number of nasty messages and told I had to cover my shift as no bereavement time was allowed for pets.”
Ms McNulty did not attend work and, she says, was recently fired, causing her “extreme distress.”
She explained: “I think it’s disgusting how some companies think it’s acceptable to treat someone in this way with no remorse, a family pet has just as much importance as a human family member.
“It’s time companies acknowledged this and give people the time they need to grieve with no worry of losing their job.”
Since starting her online petition she has received dozens of messages of support.
Daniel Taylor wrote: "Dogs are family. You should be allowed to grieve for them too."
Tracy Rawding added: "Pets are family members and the grief is very real."
Diane James, pet bereavement support service manager at Blue Cross, said: "We fully support understanding employers who offer bereavement leave to allow time for pet owners to come to terms with their loss.
"We have been helping pet owners for 25 years and are contacted by over 12,000 devastated pet owners every year who are struggling to cope."