The record 54-time Scottish champions were demoted to the country's bottom tier in 2012 because of financial problems. They won two successive promotions and qualified for a playoff for the right to return to the Scottish Premiership.
Rangers lost 3-1 in the first leg to Motherwell on Thursday, and were beaten 3-0 in the return match to lose 6-1 on aggregate.
Rangers substitute Bilel Mohsni, a Tunisia international, kicked and threw punches at Motherwell's Lee Erwin after the final whistle, sparking a mass brawl. Scottish police said the incident is being reviewed.
Mohsni, Erwin and Motherwell substitute Fraser Kerr were sent off in the tunnel.
Erwin said Mohsni reacted badly after snubbing an offer of a handshake at fulltime.
"He told me to (expletive) — I pushed him and he reacted badly," Erwin said. "A player at a club like that, at that level, should not be acting like that.
"It's embarrassing for him and the club."