Uefa has fined Rangers 40,000 euros (£35,652) and banned its fans from the next away European game for sectarian singing in a match at PSV Eindhoven.
At a hearing in Nyon, Switzerland, Uefa also gave Rangers a suspended ban on its fans for a second away game for a probationary period of three years.
Uefa also issued a suspended punishment for fans' behaviour at the Ibrox leg.
It will fine Rangers a further 40,000 euros and close Ibrox for one match if fans misbehave in the next three years.
Should the Scottish Premier League leaders choose to appeal against the decision, the club must do so within three days of receiving Uefa's written decision.
In a statement on the Rangers website, chief executive Martin Bain said: "We are bitterly disappointed that our club has been placed in a position where we are subjected to these kind of sanctions by Uefa.
"We will consider our position when we receive the written reasons for the decision which are expected in a week or so.
"The club put its own case very forcibly to Uefa and the more draconian sanctions that were recommended by the disciplinary inspector have been mitigated to a degree.
"To be clear, we condemn sectarianism and there is no doubt the mindless behaviour of an element of our support has exposed the club to a very serious situation. The people who engage in this type of behaviour are damaging the club they claim to support.
"It is abundantly clear from this decision that if there is any sectarian singing at future matches the suspended bans will take effect. Those fans who engage in such activity need to take that message on board."
When news broke of Uefa's intention to hear allegations of sectarian singing by the club's fans at the Europa League match against the Dutch side on 17 March, Bain said the club was "absolutely astounded" and that it planned to defend the club's position "very, very vigorously".
While acknowledging that sectarian singing is a problem among a section of its support, Bain had argued that the club had taken significant steps to wipe out such behaviour.
He also said Rangers were unhappy that a report from FARE (Football Against Racism in Europe) should result in them facing charges, while the Uefa match delegates gave favourable reports on its fans' behaviour in the games against PSV.
However, Piara Powar, executive director of the FARE network, earlier this month defended his organisation and denied there was any undue focus on Rangers.
"The FARE network is focused only on our core mission of tackling discrimination in football and encouraging social inclusion through the game," he said.
"We have no axe to grind with any club."
Bain added in Thursday's response to Uefa's sanctions: "In terms of the Uefa case brought against us, we have had serious concerns about the integrity of the evidence compiled by the FARE organisation and that remains the case.
"We are also of the opinion that FARE has been influenced by people who make it their business to damage our club in any way they can.
"We are committed to the eradication of sectarianism and believe it would have been more constructive for FARE to work with our club rather than against it.
"Instead, they submitted evidence to Uefa with a clear objective in mind and have shown a complete lack of transparency or accountability when asked for clarification on various aspects of that evidence."
Earlier on Thursday, Rangers assistant manager Ally McCoist accepted that if a ban on fans attending matches at Ibrox helped to eradicate sectarianism, it would be worth the club taking the financial hit.
He said ahead of Uefa's decision: "No matter what it costs, if the problem can get eradicated, then anything is a good thing."
McCoist, though, believes the guilty fans should be punished instead of the club.
"It would be a real blow," added McCoist. "The atmosphere at our place in the Champions League in recent seasons has been out of this world.
"I'd feel really sorry for the good fans and the players as well."
The decision by Uefa's Control and Disciplinary Body to punish Rangers will have been based in part on the club's fans' behavioural record over the past five years.
The Glasgow club was fined £13,300 for supporters' discriminatory chanting and £9,000 for attacking their opponents' team bus during an away game against Villarreal in 2006.
And Uefa issued a fine of £8,280 for some Rangers fans' behaviour during a match against Osasuna in May 2007.
The following year, at the Uefa Cup final in Manchester, fans were involved in city centre riots, and a fine of £18,000 was imposed by Uefa for fan violence when the club played Unirea Urziceni in Romania in November 2009.