Forest eventually emerged victorious from a thrilling encounter at the City Ground which finished 3-3 after extra-time, with the Championship outfit progressing into the second round after triumphing 4-3 in a dramatic penalty shoot-out.
Craig Westcarr sent the tie into added time after Lewis McGugan and Robbie Findley had cancelled out Mike Edwards' early opener.
Lee Hughes' strike then looked to have won it for County before Wes Morgan levelled in the 122nd minute with a sensational 25-yard finish.
Hughes had the chance to win the subsequent shoot-out for his side following George Boateng's miss, but the striker lifted his penalty over the bar and team-mate Neal Bishop swiftly followed suit to hand Forest victory.
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."