Steve McClaren's post-match analysis will throw up different problems to those posed by Saturday's game against Barnsley as League One side County caused the Reds' plenty of headaches at the back with their positive approach to the game.
Lewis McGugan's superb strike equalised Edwards' early goal for the visitors before Robbie Findley netted to put Forest in front.
Craig Westcarr and Lee Hughes looked to have secured a famous victory for the Magpies before a dramatic leveller from Wes Morgan in the 123rd minute of the match.
Notts then missed a chance to win the shoot-out before Luke Chambers netted what proved to be the winning spot-kick for the Reds, Bishop blazing over for County.
Afterwards McClaren told Sky Sports News: "This game certainly tests your nerves.
"I've said to the players when you follow me it's a rollercoaster, and that's what it was.
"What a great game, for the neutral, and for both sets of fans, fantastic. For the manager and the coaches, a nightmare.
"But in the end we came out on top. It was like a boxing match, toe-to-toe, slugging it out, not giving an inch, and we were the ones left standing."
A League Cup win at least makes up for what had previously been a bad day at the office for McClaren who, after singing his praises to the press, saw Dutch winger Wesley Verhoek pull out of a £2m move to the City Ground.