The Colombian international was shown a straight red card for catching Hoops captain Scott Brown with an elbow and has been hit with a four-match ban as a result of the sending-off.
The 22-year-old posted a statement on his Twitter account, saying: “I would like to offer an apology to all the fans, my team-mates and the coaching staff for what happened in yesterday’s match.
“I promise to do everything in my power to ensure that nothing like that happens again and to give the club and the fans my all.
“Thanks for the support and affection you’ve always given me.”
Morelos is suspended for two matches but has had an additional two tacked on as a result of previous red-card offences.
Light Blues boss Steven Gerrard told RangersTV after the match: “[Alfredo] will be punished internally and we’ll move forward.
“The reality is if you raise your arm, you leave yourself wide open. Obviously he’s been provoked in the first place but it’s happened on too many occasions now.
“I’ve gone above and beyond - I’ve backed Alfredo more than enough and I can’t defend him any more.”
It was Morelos’s fifth red card of the season, albeit one was rescinded on appeal. His first of the campaign - for kicking out at Aberdeen defender Scott McKenna on the opening day of the season - was overturned.
But he has been sent off on two other occasions against the Dons this term - once for lashing out at Graeme Shinnie, and again for clashing with McKenna, with the Dons defender also seeing red.
The former HJK Helsinki forward was also sent off during the Gers’ Europa League clash with Russian side FC Ufa. Morelos was booked for kicking the ball away before receiving a second caution and subsequent red card for dissent.