The store has been operating for close to two centuries and is reportedly the oldest independent department store in the world.
The firm said the business was no longer sustainable in the long term.
Fifty-three staff members are losing their jobs as a result.
The shutters came down on the iconic department store on Tuesday.
Politicians and business leaders have expressed their dismay at the news.
SDLP leader and Foyle MLA Colum Eastwood has said the closure of the city centre landmark is a “shock to local retailing and our thoughts are with the staff affected by its closure”.
“I will immediately be in contact with all relevant authorities to ensure that the staff are given all the support and help they require as they come to terms with today’s news and as they begin the search for new employment.
“A struggling economy will always result in a struggling retail sector. Derry’s economy is struggling and the sudden closure of Austins is testament to that.
“The failure of the Executive to properly invest in the West has left a legacy of economic stagnation and the impact of this has been felt by the staff of Austins today. The closure of Austins is sorely symbolic of this failure.”
Foyle DUP MLA Gary Middleton has expressed his sadness, saying Austins “is part of the fabric of Londondery”.
“The business has served generations of people in the city and beyond, and I am saddened to hear that it has gone into liquidation,” he said.
“Some of the staff who work in the shop contacted me this morning when they arrived for work and found the shutters were down. It is obviously very distressing for them, particularly given they had no prior warning.
“If there is anything which can be done either to assist the company, and particularly to help those staff who face a very uncertain time, then I will do all in my power to help.”
The Northern Ireland Independent Retail Trade Association (NIIRTA) has said Austins shutting up shop is big loss to the independent retail sector.
Chief Executive Glyn Roberts said: “This is truly dreadful news that one of oldest independent retailers in Europe is to close its doors after 186 years of trading in Londonderry”
“This is not just a loss for Derry, but to Northern Ireland’s independent retail sector as whole.
“Austins was very much a destination retailer for Derry City Centre and its closure will result in less footfall for the surrounding local traders. Our thoughts are with the fifty three Austins staff and their families at this difficult time.”
He added: “It underlines the need for the NI Executive and Derry & Strabane Council to have a coordinated strategy to address the many challenges facing Londonderry City Centre and its traders”