However, the gallant Highlanders, who cancelled out Nish's seventh-minute strike with an own goal from Ian Murray, fully merited a 2-2 draw and the replay on Tuesday week that gives them the chance of joining fellow First Division outfit Raith Rovers in booking a trip to Hampden.
After dominating the second half and snatching an equaliser 11 minutes from time through striker Michael Gardyne, Stack was then called on to save Martin Scott's shot bravely with his face after the visitors' midfielder had seen his first effort cleared off the line by Murray.
The former Arsenal goalkeeper admitted the Edinburgh club's long hoodoo in the competition had made the result doubly disappointing and he knows John Hughes' side will have to match County's fighting spirit if they are to win next week's rematch.
He said: "The biggest difference between them and us was their work ethic. Their desire to go through to the next round and go on and win the game was far greater than ours.
"We're very disappointed. Everyone knows what's at stake here. It's not just a normal cup run, we know the history of the cup and we know how long it's been.
"Every one of us was disappointed and the gaffer was disappointed and angry, and rightly so.
"It's frustrating when we had put ourselves in such a great position to put ourselves in the next round of the cup and play at Hampden, which is a dream for me - it's something I've wanted to do since I've been here.
"We lived life on the edge and maybe in the end we were fortunate to come away still in the hat.
"But there were lessons to be learned. We all know where we went wrong, there are a lot of individuals who might feel they let themselves down, and we've got an opportunity to go and turn that round when we go there the next time."
Nish headed in Chris Hogg's bouncing shot after a goalmouth scramble but Ross County equalised when Gardyne's shot was saved by Stack the rebound ricocheted off Murray and into his own net.
Only three minutes later, Hibs restored their lead when Riordan collected John Rankin's pass on the edge of the box and beat Michael McGovern but Gardyne secured a replay when he was first to react to Paul Lawson's looped pass.
Gardyne is now hopeful of making it through to the semi-finals.
He said: "Right from the start the performance was brilliant. Hibs saw pretty much the best of us on Saturday and I'm not sure if they will fancy coming all the way up to Dingwall.
"We'll be well up for it and they will need to be up for it.
"The boys are soaring in confidence after Saturday and everybody will be looking forward to the replay.
"It would be great if we could match what we did on Saturday. If we do we've got every chance to sneak through."
Source: Team Talk
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