Thousands of low income families with a disabled child were paid up to £4,400 too little in tax credits after data was not shared between authorities.
Some 28,000 families received at least £3,000 too little from 2011-2014 after the Department for Work and Pensions failed to inform the HMRC they were eligible for the extra money.
HMRC said it would repay the money owed for 2016-17 but not for earlier years.
It said it was up to individuals to check they received the right payments.
The families who missed out on payments were those with a disabled child who qualified for Disability Living Allowance and who also receive tax credits - a means-tested top-up for low income households.
They should get an extra £3,100 a year or £4,400 a year depending on the severity of the child's disability.
But about one in 12 families did not receive the payment after the information was not shared between the DWP and HMRC, an audit found.
The DWP is responsible for disability benefits, while the HMRC pays out tax credits.
Paying back the families the money they lost this year will cost the government £95m.
HMRC told BBC Radio 4's Money Box that it would repay the money from 2016-17 and ensure it was paid in future years but it would not pay the money for previous years.
It said it was up to individuals to claim the right amount and, when it is awarded, check it is correct.
- Money Box is broadcast on BBC Radio 4 at 12:00 GMT