Durban House, which explored the writer's life, was closed by Broxtowe Borough Council to save Â£80,000 a year.
The authority said the service had not stopped and would merge with Lawrence's birthplace museum in the same town.
Malcolm Gray, chairman of the DH Lawrence Society, said it was a "frustrating" decision.
Alex Khan, cultural services manager at the Conservative-led council, said: "I actually find it quite exciting - it puts the focus of the DH Lawrence Heritage service back somewhere it has a very strong link.
"Lawrence was born there, we've got artefacts that relate to his life and his family and Victorian life - it's a great place to learn about British history as well as about literature and the Lawrence family."
Mr Khan denied the closure was "a slap in the face" following Nottingham's status as a Unesco City of Literature, awarded in December.
However, Mr Gray, who described the writer of Lady Chatterley's Lover as the "greatest author in the English language", said the closure was "disappointing".
"More could have been done in the past to promote the centre, opportunities have been missed," he said.
He said Lawrence's birthplace was too small and had little room to accommodate a school group.
Mr Gray added that the society would "keep fighting" the decision.
The campaign to keep Durban House open was led by Labour MP Gloria De Piero, and supported by screenwriter William Ivory, double Oscar-winning actress Glenda Jackson and actor Robert Lindsay.
The closure of the DH Lawrence Heritage Centre in Eastwood has been described as "tragic" by a society that promotes the author's work.