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.
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 told BBC Radio Scotland: "We have seen games go ahead in far worse circumstances and we are very, very disappointed to say the least.
"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."
Hearts' disappointment was no doubt exacerbated by the fact that a full Highland League card took place on Saturday afternoon.
But Ross County chairman Roy MacGregor accepted Brines' decision on the grounds of safety concerns for the players and made a generous attempt to help the disappointed travelling fans.
He said: "I've offered to pay for the Hearts supporters to come up here free of charge to the replay.
"We are both out of the Scottish Cup so we've offered them the February 2 or on March 6, which are both Saturdays - it will be easier for the Hearts supporters.
"We are a community club here that does feel for fans - it cost them not just for a ticket, which is expensive enough, but to come here.
"We've gone out of our way to show some respect and some sort of appreciation to the fans who travelled from Edinburgh today.
"We are also really disappointed for our own supporters - it is holiday time and they would have been looking forward to a game."