The Home Office has been accused of "complacency" and shirking its responsibility in response to the Windrush scandal.
A report by the Commons Public Accounts Committee (PAC) said the department had failed to "take ownership" of problems it had created.
The scandal involved wrongful detentions and deportations of some members of the Windrush generation.
The Home Office said it was determined to "right the wrongs" experienced.
PAC chairwoman Meg Hillier said: "It is deeply regrettable that a scandal of this magnitude, on the back of repeated and unheeded warnings, does not appear to have fully shaken the Home Office out of its complacency about its systemic and cultural problems."
She said that "there is a long way to go before the Home Office can credibly claim to have put things right".
The committee of MPs also criticised a decision to exclude up to 160,000 non-Caribbean Commonwealth cases from a review carried out to identify how many people may have been affected.
A review of 11,800 Caribbean cases identified 164 who were removed or detained who might have been resident in the UK before 1973.
But the report warned that the Windrush scandal concerned the entire Commonwealth and other cases could not be "simply ignored".
An estimated 500,000 people now living in the UK who arrived between 1948 and 1971 from Caribbean countries have been called the Windrush generation, in reference to a ship which brought workers to the UK in 1948.
They were granted indefinite leave to remain in 1971 but thousands were children travelling on their parents' passports, without their own documents.
Changes to immigration law in 2012 meant those without documents were asked for evidence to continue working, access services or even to remain in the UK.
Some were held in detention or removed despite living in the country for decades, resulting in a furious backlash over their treatment.
The MPs' report condemned the department for failing to keep accurate records of people's immigration status and showing a "lack of concern" about the impact its policies had.
It also said the Home Office had lacked "any sense of urgency" in its response to the scandal and took eight months to set up a hardship fund, adding that a compensation scheme is still not operating over a year since the problems were first exposed.
A Home Office spokeswoman said a dedicated taskforce had helped thousands prove their status in the UK and had provided support to more than 600 people on issues including benefits and housing.
She said the home secretary had also commissioned a review with independent oversight to establish what went wrong and prevent it happening again.