County parted company with Derek Adams and his father George, the club's director of football, on Thursday but suffered a 4-0 loss at high-flying Hamilton.
Reports in the Scottish media have linked former Netherlands international Patrick Kulivert - who was assistant to Louis van Gaal at the World Cup in Brazil - with the vacancy, but whoever Adams' successor is has a huge job on their hands to reverse a run of five consecutive league losses.
Under the guidance of coach Steve Ferguson and captain Richie Brittain, County were more than a match for their hosts before the break, but a second-half capitulation exposed some familiar flaws.
Martin Canning headed in the opener two minutes after the interval and Mickael Antoine-Curier scored two penalties, with Uros Celcer given his marching orders for conceding the second.
Brittain then missed a spot-kick and Jason Scotland added the fourth to keep Hamilton in second place and compound County's misery.
Inverness Caledonian Thistle remain top of the pile courtesy of a 2-0 win over Kilmarnock, Aaron Doran and Greg Tansey netting second-half goals for the leaders.
John Hughes' men are still unbeaten in the league and sit seven points clear of Celtic - who they beat last Saturday - though the champions have two games in hand.
Dundee United round off the top three following a 3-0 win at St Mirren, who remain Ross County on no points.
Elsewhere, loanee Brian Graham scored on his St Johnstone debut in a 1-0 win over Motherwell, and Aberdeen beat Partick Thistle 2-0.
Celtic travel to Dundee on Sunday as Ronny Deila's side seek to put their failure to qualify for the UEFA Champions League group stages behind them.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.