The rampant Hoops fired in nine without reply at Tannadice on Sunday and with United having picked up just one point this season, it proved to be the final straw.
Ross said after the game he was determined to put things right.
He told Sky Sports: “We owe the supporters an apology because of the manner of the scoreline and the manner of the goals we concede. And large aspects of the performance were not reflective of wearing a jersey in professional football.
“Secondly, my determination to put this right will remain consistent. I’ve done this for a long time and worked in a consistent manner.
“So when I talk about being humiliated and embarrassed, I want to fix that. You need to have faith in your managerial ability through previous experiences and the challenges I have overcome in my football and coaching career. It’s not in my character not to believe I can do it and not to want to do it.”
Tangarines sporting director Tony Asghar had come out in support of Ross last week after unfounded rumours surfaced that the manager had quit.
However, the nature of the latest defeat appears to have forced the club’s hand and a brief statement from the club on Tuesday morning read: “Dundee United can confirm head coach Jack Ross has been relieved of his duties with immediate effect.
“Liam Fox will take charge of the the first team on an interim basis with the focus now fully on Wednesday’s Premier Sports Cup match with Livingston.
“No further comment will be issued by Dundee United at this stage.”
Former Hibs and Sunderland boss Ross took the United job in June, six months after his departure from Easter Road.
The campaign began with a 1-1 draw at Kilmarnock but that was followed up by four straight defeats, culminating in that 9-0 battering by Celtic.
In between, the Tangarines’ European exploits were cut short after a 1-0 home win over AZ Alkmaar was overturned in emphatic fashion by the Dutch side, who won 7-0 in the return fixture.