Morelos was left out of Saturday's quarter-final defeat by Hearts after arriving back 24 hours late from a trip to see his sick mother in Colombia on Thursday.
In a statement on his Twitter account, Morelos said: "I wish to apologise to the club, the manager, coaching staff, all of my teammates and the Rangers fans for disappointing them with my conduct last week.
"I understand that people inside and outside the club are disappointed that I let them down and it was never my intention to do so.
"Everyone at Rangers and the fans have given me so much love that I'm so grateful for and I just want to show everyone on the pitch how much Rangers means to me."
Light Blues boss Steven Gerrard earlier confirmed Morelos was back in his plans for Wednesday's Ladbrokes Premiership visit of Hamilton after being disciplined.
"He has been disciplined internally, which he has accepted and he has shown a lot of remorse for his actions, letting his team-mates down and supporters down," Gerrard said.
It was the latest costly piece of ill-discipline from the 23-year-old, who has been sent off seven times in little over 18 months albeit one red card was later rescinded.