The Robins already knew they would be playing in League One next season but O'Driscoll felt their lack of effort was hard to defend.
On-loan Norwich striker James Vaughan helped himself to a hat-trick for the Terriers, with Lewin Nyatanga's stoppage-time headed goal scant consolation for the home side.
"That performance was the worst since I came here and totally unacceptable," said O'Driscoll.
"We played without pride and I can assure supporters that won't happen again.
"We owe them an apology. In our last game at Hull we looked as though we shouldn't be relegated, but today we showed why we are going down.
"Basically we are not good enough. The home performances since I took over have been consistently encouraging, even when we have been beaten.
"Losses are inevitable at times and it is how you lose that counts. We have a lot of work to do during the summer and need to man-up."