The Victoria Park surface was inspected twice by referee Iain Brines following heavy rain showers and he decided to call off the game after his second check.
County have offered to pay for Hearts fans to travel to the rearranged game, with Scottish Cup Saturdays on 2 February and 6 March being mooted as potential dates.
But Hearts boss John McGlynn felt for the estimated 800 visiting supporters who were well on their way to Dingwall when the news broke.
McGlynn said: "We had no indication whatsoever that the game was in any difficulty. Our kit man left the hotel this morning at the back of 10. Nobody said to him there was a problem.
"There was people working on the pitch, who were doing their best to get the match playable. He phoned me at the back of 12 to tell me Ross County were looking for a pitch inspection.
"My problem is with the pitch inspection, it should have been done earlier. They gave us no indication there was a problem whatsoever until the back of 12.
"The referee felt the area front of the main stand was the only problem area on the pitch. At two o'clock he said the ball wasn't bouncing in that area and due to that and the weather forecast, which was for more rain, he had to postpone the game."
County chairman Roy MacGregor said: "The safety of the players is important, we're all disappointed. The referee was in a position if he put the game on and a player was badly hurt he would have had some difficulty."