The keeper has been charged retrospectively last week after kicking out at the LeWIS Ferguson of Aberdeen.
37, mcGregor, contested your choice, however, it was upheld at Hampden at a hearing Wednesday.
“Rangers does not have any option but to simply accept this decision,” a statement .
“But, it’s abundantly clear questions regarding the recent disciplinary system, which we believe is flawed, has to be introduced.
“Rangers has been in dialogue with the Scottish FA on this topic for a while and would advocate that the system is currently thoroughly assessed as a matter of extreme urgency”
The trip of S T Johnstone will be missed by mcGregor against Kilmarnock on the Scottish Cup fourth-round replay and Saturday.
The Ibrox side lost their appeal against the red card shown to Alfredo Morelos at the 4-2 win at Pittodrie.
Former Rangers striker Billy Dodds on Sportsound:
I am aware Allan McGregor well. He’s a fantastic lad but he has developed a habit of picking up people that are shoulder-charging and the ball. He enjoys to leave a bit onto you. It is the first time that I have seen him do that with his foot. I presume they’ve predicted it properly.
Former Celtic striker Scott McDonald on Sportsound:
Somewhere else on the field it’s a direct red card. An opponent is being endangered by it. He has already got the ball into his hands and he has gone with a leg. LeWIS Ferguson is really just a blessed boy. He could have done worse injury.