The club have been ordered to close part of Ibrox for Thursday’s Europa League meeting with Legia Warsaw.
Clarke said he faced “sectarian” abuse from the “dark ages” at the ground last season while in charge of Kilmarnock.
“Maybe it will make some people think about what they’re going to say in the future, hopefully,” he said.
“There are other people get it from the Celtic fans,” he told BBC Scotland. “It’s not a one-way street. It’s two different sides, two different clubs, two fantastic clubs, but they have to do a little bit more to stamp it out.
“Rangers have reacted very well to it. They’re trying their best, as I’m sure the people at Celtic are.”
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‘Sometimes clubs have to try a little harder’
Rangers chairman Dave King apologised publicly to Clarke after February’s 5-0 defeat in Govan. He also issued a strongly-worded statement in response to the UEFA punishment that means 3,000 seats on Thursday will be closed off, urging any supporter “unable to behave in a civilised manner” to “stay away from Ibrox and our club”.
“I’ve been back at Ibrox since – no issues whatsoever,” Clarke. “I had some wonderful supportive letters from Rangers supporters and not too many disruptive letters.
“I was actually very heartened by the response I got from a lot of people all over Scotland.”.
The Scotland manager believes Hearts owner Ann Budge’s decision to close a section of Tynecastle last season helped the club tackle fan misbehaviour, adding: “The clubs have to clamp down on it. And the clubs do try, but sometimes they maybe have to try a little bit harder.
“I thought the move by Ann Budge was brave and it’s worked well for them because it gives people a little lesson and says ‘look, you can’t go into a football stadium and behave like an idiot’. You have to go into a stadium, support your team, sing all the songs that are supportive of your own team, rather than try to be negative towards the opposition.”
‘Suddenly it’s not a crime’
Clarke says he “lost it” in an emotional press conference after Kilmarnock’s 5-0 defeat back in February.
“I’d come back to Scotland and you think times would move on, Rangers were much more inclusive,” said the former Chelsea defender.
“To get that on that particular night, listen, the chants started, it was fine, I was whatever I was, I was a ‘W’, no problem, it was their night.
“They [supporters] deserved their moment, I was happy to take that, but the sectarian singing, you don’t need. If it happens in the street, it’s a crime. If it happens in a football stadium, there are so many people doing it then suddenly it’s not a crime. That can’t be correct.
“I would love to think that in years to come it won’t be an issue in Scotland and hopefully with education, with time, it will get better and become a thing of the past.”