The Rams posed the greater threat during a keenly-contested first half at the iPro Stadium, and took an early lead when Henri Lansbury nodded into his own net.
Promotion-chasing Derby were unable to contain Forest after the interval, though, with Buxton of the opinion that the visitors became more direct.
The pressure they were able to put the hosts under eventually lead to them buckling late on, with Britt Assombalonga and Ben Osborn turning the tie on its head.
Buxton admits Derby lacked the required ‘bottle’ to see the game out and paid the price for failing to keep their intensity levels high.
He told Rams Player: “It’s disappointing not just to lose at home, but to do it against our local rivals.
“In the first half we controlled and dictated the play. We were more compact, we had the quality and we brought the ball under control. I thought we looked a real threat.”
“In the second half, it was like we took our foot right off the gas. We played the long ball game and played right into their hands.
“They knew that they were losing out in midfield in the first half, so after half time they went route one, headed everything, picked things up better and they were a threat.
“They were obviously fighting and scrapping and what we needed to do was play our football, but we lost our bottle.”
Despite suffering a rare defeat, Derby sit third in the second-tier standings.
Bournemouth have pulled three points clear of the Rams and one ahead of Ipswich Town at the summit.
McClaren must wait until January 27 before getting the chance to offer a positive response to derby defeat in the league, with the FA Cup taking centre stage next weekend as Derby take in another meeting with a local foe in the form of Chesterfield.