The Glasgow giants appeared to be on track for the victory at Shielfield yesterday when Andy Little claimed his seventh goal of the season on the stroke of half-time.
But the home side fought back thanks to a leveller from substitute Fraser McLaren and could have claimed the three points when Chris Townsley’s injury-time goal was disallowed for a foul in the build-up that appeared to be a debatable call by referee Mike Tumilty.
McCoist said: “That performance is absolutely miles short. It was unacceptable.”
Hearts missed out on the chance to go top of the Clydesdale Bank Premier League as they were held to a goalless draw against Aberdeen at Pittodrie.
In yesterday’s other game in the Scottish top flight, Thomas Reilly’s stoppage-time leveller handed St Mirren a 1-1 draw against Motherwell at Fir Park.
Micheal Higdon had put the home side ahead in the first minute.
Tony Watt scored a double on his first Celtic start as Neil Lennon’s injury-hit champions beat Inverness 4-2 on Saturday.
The 18-year-old produced a composed finish in the 24th minute to add to Victor Wanyama’s early headed opener.
Charlie Mulgrew fired Celtic three ahead just after the break and Watt was on hand to make it 4-0 in the 64th minute.
However, the Hoops switched off the final 10 minutes and Ross Draper scored two consolations.