The Scottish international was targeted by two men as he shopped alone in a supermarket the day before Celtic’s 3-2 victory at Ibrox.
Filming the incident, the men called Martin a “h** p***k” and an “orange b*****d” as they passed.
The following day Celtic star Scott Sinclair was then abused by three men in an airport lounge.
The two incidents gave a reminder as to the problems associated with Scotland’s biggest rivalry, though Martin says he won’t let it affect him as he looks to remain with Rangers on a long-term basis.
“It is what it is, to be honest,” said the Norwich City loanee. “I didn’t think anything of it until I got a phone call asking about it.
“It’s disappointing for sure, but it’s not indicative of the people up here. It’s not what I have found the city to be like.
“It’s a really small minority and we move on.
“I’ve made it known that I want to stay, so I’ll have to keep doing well enough to make sure that happens.”