Crowd trouble marred the end of the Scottish Cup final as Hibernian ended a 114-year wait to win the trophy.
Rangers said players and staff were assaulted by Hibs fans who invaded the pitch.
The club commended its own supporters for showing restraint under “severe provocation”.
A statement said: “Rangers Football Club is shocked at the disgraceful behaviour of Hibs fans at full time.
“Rangers players and staff were assaulted by these fans who invaded the pitch and in the interests of their safety could not return to the pitch for the medal presentation.
“There can be no place for the violent behaviour witnessed at the end of the final and Rangers fully expect the Scottish Football Association and Police Scotland to launch an investigation to find out where security measures failed.
“The club would like to commend Rangers fans for the restraint the showed under severe provocation.”
Stewart Regan, chief executive of the Scottish Football Association, said the body was ‘’appalled by the scenes of disorder and the contemptible behaviour’’ after the final and that a full investigation would be carried out along with Police Scotland.
Speaking after the match, Hibernian boss Alan Stubbs told Sky: “I wish all the fans had left the pitch so we could celebrate it properly.
“We don’t condone what has just happened, but that is 114 years of hurt.
“Everyone’s safety is the most important thing. I can understand the euphoria that surrounded it. I don’t condone it, but I understand it.”