Hibs lost 1-0 at Tynecastle to their administration-hit rivals' youthful side in their second Scottish Premiership game of the season.
The result followed on from their opening defeat against Motherwell and their Europa League humiliation against Malmo but Hibs are unbeaten in six games since that loss.
And McGivern is looking at the Easter Road clash at the end of October as an opportunity to atone for that August disappointment.
The Northern Ireland international said: "It's the draw all the fans would have wanted, and the players as well, it's a massive draw.
"It's a chance to set the record straight for the result earlier in the season.
"Hopefully we can do that with a sell-out crowd in a midweek game. And a cup match adds a bit more spice."
Speaking of the August defeat, McGivern said: "I came on at half-time in that game.
"I was just coming back from injury and it wasn't an ideal game to go back into it, but this is a chance to set the record straight and give the fans something to cheer about."
The Hampden draw continued a sequence of cup derbies between the Edinburgh clubs, the most famous of which was Hibs' 5-1 thrashing by the Gorgie side in the 2012 William Hill Scottish Cup final.
Hibs gained limited revenge months later when they knocked the holders out with a 1-0 fourth-round win at Easter Road.
"That was my first derby game, it was a really enjoyable game to play in," McGivern said.
"Hopefully we can get a similar result in the League Cup and a performance to match."
Hibs boss Pat Fenlon was keen to play the draw down.
"I'm not too concerned about that at the moment," he said.
"We have a lot of big games before then and that will look after itself when it comes around."
- Sports & Recreation
- Scottish Premiership