The Terriers took the lead through James Vaughan but Radoslaw Majewski responded with a hat-trick for Forest, while Elliot Ward, Henri Lansbury and Darius Henderson were also on target at the City Ground.
Robins recently took charge after the departure of Simon Grayson and he admits his side must swiftly turn around their fortunes after they were left just two points above the drop-zone.
He said: "It's the most embarrassed I've been as a manager.
"I can't believe how naive we've been, if you want to pass the ball then that's fine but you've got to win your battles
"You try not to overact to a defeat but we need to be picking points up. It started off so well and ended up as it did but we need to pick ourselves up for Ipswich.
"We've got 14 games left and we need to start picking points up because we're in the thick of a relegation scrap."