McIntyre took over on Tuesday following the sacking of Derek Adams and could only look on as his new team slipped to a sixth consecutive Scottish Premiership defeat on Saturday.
Midfielder Iain Vigurs broke the deadlock with a free-kick after 49 minutes before forward John Sutton struck five minutes later with a superb 30-yard strike.
Striker Liam Boyce pulled one back for the hosts 12 minutes from the end, but that proved to be no more than a consolation as County's search for a first point of the season goes on.
Inverness Caledonian Thistle slipped off the top of the table with a 3-1 defeat at Partick Thistle, with goals from Steven Lawless, Abdul Osman and Kallum Higginbotham giving the hosts victory after Aaron Doran had put John Hughes' men ahead in the 13th minute.
That result sees Hamilton Academical go top of the league following a fiery 2-2 draw at Dundee United.
Turkish attacker Nadir Ciftci put United ahead at Tannadice, only for Mickael Antoine-Curier to level.
Hamilton were reduced to 10 men immediately after the goal, forward Darian McKinnon seeing red for celebrating in front of the home bench moments after being booked for an incident involving Ciftci.
Anthony Andreu then put a depleted Hamilton side in front before Jaroslaw Fojut levelled in the 45th minute, four minutes after Ciftci had received his second yellow for handling the ball into the net.
Defending champions Celtic are three points off the top, Jason Denayer and Kris Commons on target in a 2-1 success against Aberdeen, who were defeated despite David Goodwillie's second-half effort.
Elsewhere, St Mirren are still without a point following a 2-1 reverse against Kilmarnock, while Dundee won 1-0 at St Johnstone.
