Overall, Centrica posted an adjusted operating profit of £1,252m for the year, down 17%.
However, EBITDA fell by 9 per cent to £2.14bn.
The government's price cap will affect millions of British Gas customers by the end of this year, which Conn admitted would dent profit margins.
Centrica said the 4000 new job losses would be mainly within the United Kingdom energy supply area of the business.
Around 4.5 million of Centrica's customers - about 60% - were on SVTs at the time of the announcement, with 70% of profits coming from the SVT customer base. The profit margin per customer, which has ranged between £42 and £65 since 2009, remained broadly level at £59 - or around 6 per cent.
The Unite union on Thursday called for urgent meeting with British Gas after the company said it was planning more than 4,000 job cuts.
According to energy regulator Ofgem, a UK Government plan to cap the most common gas and electricity tariffs could come into effect by Christmas this year.
The latest reduction in jobs means headcount has dropped by 5,500 since the start of 2016 as the company aim to save £1.25 billion per year by 2020.
Conn said the expansion to the scope of its cost cutting efforts is partly a response to "fierce" competition in the retail market from almost 70 suppliers, "most of which lose money", as well as the trend towards online interactions with customers.
The company also faces a new energy force in the form of the merged npower and SSE, as well as new entrants with financial muscle such as Shell, which bought First Utility a year ago. He also refused to rule out further job cuts in future.
In response to 2017's "poor shareholder experience" Mr Conn said: "We regret this deeply, and I am determined to restore shareholder value and confidence". "We're not in a blame game here".
Theresa May wants to introduced a price cap for the most vulnerable households to ensure they get the best deal for their energy.
Unison, the largest union representing white collar workers at British Gas, said the firm needed to alter its strategy. "We hope it doesn't happen because we think that ultimately it will be bad for customers", he said.
Centrica intends to sell its 20 per cent stake in Britain's nuclear power plants by 2020 and could return some of the proceeds to shareholders.