Ms Campbell initially claimed she had mistaken the drug for another with a similar name, then later said she thought vets were allowed to order prescription medicine under a company policy.
A subsequent investigation revealed she had also earlier ordered the anti-pain medicines Voltaren and Brufen and was seen by a co-worker taking some cat food from the office.
Legally vets can order human prescription medicines to treat animals but not for personal use.
Authority member Eleanor Robinson said Ms Campbell was experienced enough to know she had acted illegally and found no disparity in the way her dismissal was handled.
"I have found that HVL found substantive justification for terminating Ms Campbell's employment on the basis of serious misconduct after undertaking a full and fair investigation process.
"I determine that Ms Campbell was not unjustifiably dismissed by HVL," she said.
