Hearts skipper Marius Zaliukas deflected David Wotherspoon's shot into his own net in the 83rd minute at Easter Road as their defence of the trophy ended at the first hurdle.
Hibernian's slightly fortuitous 1-0 win ended a run of 12 derby games without victory for the Leith side, who restored some more pride following their 5-1 final thrashing.
Hearts now continue their financial struggles with a tax bill of £450,000, which sparked a winding-up order, due to be settled in full on Monday.
Fans have helped raise enough money to pay Her Majesty's Revenue and Customs but there is still a shortfall in revenue for the season that totals £2million while a separate £1.75million tax bill, which the club are challenging, hangs over Tynecastle.
McGlynn said: "The priority is the football club survives and we shouldn't underestimate that. We have got to make sure the financial battle we have on our hands is one we win.
"There were a number of young players on the pitch. We have a number of other young players who are coming through. That is the way we are going, we are developing young players and giving them the opportunity to play.
"We look to try and do better in the league and we've got a semi-final of the League Cup (against Inverness) to look forward to at the end of January.
"It's disappointing to lose the Scottish Cup but we still have a lot to play for."
But McGlynn admitted their lack of goal threat could undermine their season after a third game without finding the net.
Callum Paterson had an early header saved but Hibs goalkeeper Ben Williams' only other stop of note came from a deflection off team-mate Paul Hanlon.
"The lack of goals is the thing," McGlynn, who brought striker John Sutton off the bench for the last 20 minutes, said. "It's not rocket science, we need to strengthen in that department.
"That's been the same since the first day I came in. We wanted to strengthen but, with the financial situation at the football club, we couldn't really bring anyone in.
"It's going to probably haunt us all season, I would suggest, because we need to strengthen in that department.
"It's obviously not do-able under the current situation."
Scottish Premier League Without Celtic 12/13 Without Celtic: Hearts 150/1
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