The match was called off less than an hour before Saturday's 3pm kick-off when referee Iain Brines ruled the pitch unplayable because of waterlogged patches following a second inspection.
Hearts MD David Southern told BBC Radio Scotland: "We have seen games go ahead in far worse circumstances and we are very, very disappointed to say the least."
The decision clearly came as a surprise to Southern, who described 95% of the Global Energy Stadium pitch as being in "excellent" condition while an earlier rainfall had subsided and the sun was out when kick-off approached.
But the visiting club's biggest concern was the fact Brines had not arrived in time to make a decision before an estimated 800 Hearts fans were well on their way to Dingwall.
Southern added: "My understanding is the referee arrived at the ground between one o'clock and half past one. Given the rain that has fallen across the country, would it not have been more prudent for the referee to have been here mid-morning or early morning?
"A number of fans, not just Hearts fans but Ross County fans, have travelled from far and wide.
"We have supporters clubs in Manchester, Leeds, York and London that travel for this game and it does defy belief in some ways that we can actually have a game in the most northerly point of professional league football called off just one hour before kick-off.
"I actually travelled to the game with a person I know from Australia, who travelled from Brisbane to watch Hearts over the festive period and chose this game particularly.
"Now I don't see his travel expenses accommodated and I wouldn't expect that but it just gives you an idea of the emotion behind this. Looking at the pitch, it's just utter disappointment that we can't put this game on."