The bank faces a multimillion-pound compensation bill after it accepted that it should reimburse customers who faced extra costs or were unable to take advantage of discounts on one of the biggest online shopping days of the year, Cyber Monday.
Analysts believe the bank will have to pay more than £1 billion to upgrade its systems after the latest breakdown, which brought systems to a halt for three hours on Monday and left RBS, NatWest and Ulster Bank customers locked out of their accounts.
RBS said systems had returned to normal but have so far been unable to say precisely what had caused the glitch.
Ross McEwan, who started as chief executive this month, said that a "lack of investment in its systems over decades" was behind the problems.
An RBS source said that a key period of under-investment came during Mr Goodwin's time as chief executive between 2001 and 2009 when "money was spent on acquisitions rather than integrating and improving the systems".
After RBS made waves in 2000 with its £23.6bn takeover of NatWest, a bank three times its size, it went on a spending spree of acquisitions around the world.
These included the purchase of Irish mortgage provider First Active and UK insurers Churchill Insurance, Direct Line and the disastrous takeover of Dutch rival ABN Amro.
The takeover played a major part in the decline of RBS in 2008, which saw the taxpayer stump up £45.5 billion to prevent it from collapse and left the bank 80% owned by the State.
A source said: "There was a critical period of underinvestment after the purchase of NatWest up to 2009."
Millions of customers were similarly affected in June 2012 by problems with online banking and payments after a software upgrade went wrong.
That cost the bank £175m in compensation for customers and extra payments to staff after the bank opened branches for longer in response.
Stephen Hester, chief executive at the time, waived his 2012 bonus to appease customers.
The City regulator the Financial Conduct Authority is still investigating the failure that affected a total of 17 million accounts and could fine the bank.
Mr McEwan, forced into an embarrassing apology by the latest failure, said: "The systems failure was unacceptable. Yesterday was a busy shopping day and far too many of our customers were let down, unable to make purchases and withdraw cash.
"For decades, RBS failed to invest properly in its systems. We need to put our customers' needs at the centre of all we do. It will take time, but we are investing heavily in building IT systems our customers can rely on.
"I'm sorry for the inconvenience we caused our customers. We know we have to do better. I will be outlining plans in the New Year for making RBS the bank that our customers and the UK need it to be.
"This will include an outline of where we intend to invest for the future."
The bank has promised to pay compensation where customers can demonstrate they have lost out due to the problems.
In 2012 RBS set aside £125m to pay claims, but no figure has been given this time.