A statement from the Parkhead club branded the apology "inadequate", claiming it "does not identify the source of the translation or why phrases, which bore no relationship to the words used by Mr Morelos, were introduced into it".
A senior Celtic figure added: "The use of mis-translation to convey false meaning is a dangerous form of “fake news” which must be condemned and sanctioned."
Sky Sports initially published an exclusive one-to-one interview with the Colombian internationalist, asking the player questions which he answered in Spanish. The broadcaster provided subtitles, some of which bore little or no relation to the 23-year-old's responses.
In one segment, according to the translated answers, Morelos claimed he had been the victim of racial abuse from Celtic fans, which was incorrect.
Asked by the interviewer, "How often do you experience racist abuse from a crowd?" Morelos replied: "I feel there are lots of racist gestures aimed at me. At Aberdeen, for instance, they insulted my mother, me, they threw coins at me. People often throw things at me when I score at away games."
Sky Sports' original translation suggested that Morelos was accusing Celtic supporters of subjecting him to the abuse.
The broadcaster yesterday issued an apology to the player as well as Celtic and Rangers, saying: "We have identified inaccuracies in the translation of Sky Sports News' interview with Alfredo Morelos. We apologise to both Celtic and Rangers football clubs as well as Alfredo Morelos for the issues caused by these errors.
"After numerous steps undertaken by Sky to verify the interview thoroughly we can be clear that at no point did Morelos allege that any racial abuse was directed at him by Celtic supporters in the interview. We apologise to the supporters of Celtic Football Club for this serious error.
"We are reviewing our procedures for translated interviews to ensure this does not occur in future."
However, Hoops chiefs are unhappy with the response and have lodged an official complaint with broadcasting regulator Ofcom.
The champions have published their letter to the watchdog in full on their website.
Part of the letter states: "Mr Morelos spoke in Spanish and sub-titles were provided. It is our contention that the presentation of this interview was grossly and irresponsibly misleading due to the wildly inaccurate and tendentious translation which was provided in the sub-titles.
"The effect and, we believe, purpose of this misrepresentation was to broadcast offensive and incendiary allegations against Celtic Football Club and its supporters, by attempting to attribute these – quite unfairly – to Mr Morelos. It is difficult to think of a more irresponsible piece of “sporting journalism”.
"Celtic Football Club has issued a statement on the subject which is attached for your convenience. We understand that the interview is no longer available through Sky Television which is, in itself, recognition of its deficiencies. On the basis of the inaccurate translation, highly damaging and wholly inaccurate stories were briefed to the press."
The letter demands to know who was responsible for the inaccurate translation, what steps Sky took to gauge the accuracy of the translation and what part the broadcaster played in briefing the story to the wider media.
It also states: "Issues of racism and sectarianism are far too important to be manipulated in this way by any broadcaster or third party" and claims: "Mr Morelos has been seriously misrepreesented and is deserving of apology and explanation."