First-team players Nathan Patterson Calvin Bassey, Bongani Zungu and loaned-out pair Brian Kinnear and Dapo Mebude must serve immediate four-game suspensions.
The players were initially handed six-game bans – with two of those matches suspended – by a Scottish Football Association disciplinary panel, and those punishments still stand.
A statement from Rangers read: “We remain disappointed in the result. Furthermore, we believe this outcome highlights the inconsistency of decision-making in the Scottish FA’s disciplinary process.
“We are cognisant that the approach taken by other football associations across Europe has no resemblance to that of the Scottish FA.
“We urge the Scottish FA to be open-minded to learn from other football authorities.”
The five players were given police fines for attending a house gathering during lockdown in the early hours of February 14, and SFA bans were announced on March 30 after they were found guilty of breaking SFA rules and not acting in the best interests of football.
Rangers appealed and Patterson played three games before the appeal hearing on Tuesday evening, including Sunday’s Scottish Cup win over Celtic, before he and Bassey played against St Johnstone on Wednesday.
Patterson, Bassey and on-loan Zungu will now miss Sunday’s Scottish Cup quarter-final against St Johnstone, a league game against Celtic and potentially a semi-final among their four matches.
Rangers boss Steven Gerrard had accused the SFA of “guessing” and being inconsistent with the initial punishments.
He highlighted breaches by eight Aberdeen players, who did not miss any games after a night out, and Celtic defender Boli Bolingoli, who served a three-match ban after facing Kilmarnock following a secret trip to Spain.
Patterson had been playing regularly before his ban amid an injury to fellow right-back James Tavernier but the skipper returned to action in Perth.
And former Rangers midfielder and manager Stuart McCall believes the ban could scupper the 19-year-old’s chances of making Scotland’s Euro 2020 squad.
McCall – speaking at an event to promote Premier Sports’ weekend Scottish Cup coverage – said: “If Nathan could have stayed in the forefront of people’s minds by playing and playing as well as he has done, he’d have had a chance.
“He’s only put in about a dozen performances but he’s been getting better and better, which we saw in the Old Firm game. There was a lot of maturity about his performance.
“For the right-back position, Stephen O’Donnell has been doing terrifically well and Liam Palmer is in the squad too.
“I don’t think Nathan would let anyone down as he’s developed really well. I’ve seen what everyone else has seen of him and you don’t want him to be a one-season wonder, which I’m sure he won’t be.
“You just listen to what’s coming from Steven Gerrard about the way he’s been training. He sees him up close and personal every day. He trusts him so I think the kid has a very bright future ahead of him.
“But I just think the lack of opportunities between now and the end of the season to really push his case for the Euros might hamper his cause.”
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