The Home Secretary is under fire for the blunder which was caused by human error.
More than 400,000 records were wiped triggering warnings that criminal investigations could be compromised.
Asked by a member of the public whether the Home Secretary should resign over the matter, Nick Thomas-Symonds told the Fabian Society conference : “A cabinet minister who actually took responsibility for their own department would be a novelty in this Government, I am sad to say.
“There was a time when ministers did take responsibility and, of course, I would take responsibility as the home secretary for what happens in the department and my responsibility to put it right.”
He added: “Far from having a Home Secretary that takes responsibility, the Home Secretary hasn’t even appeared in public since this crisis broke on Thursday night – indeed we had to learn about it from the newspapers rather than learn from it actually from her and what she was going to do about it.
“Ministers in this Government, I am afraid, just don’t take responsibility. There is a culture of not taking responsibility and it is corrosive, frankly, to the quality of governance right across the Cabinet.”
Data was wiped from the Police National Computer (PNC) - which stores and shares criminal records information across the UK - after being inadvertently flagged for deletion.
The PNC is used in police investigations and provides real-time checks on people, vehicles and crimes, as well as whether suspects are wanted for any unsolved offences.
The coding that caused the problem was introduced in November 2020, and the deletions started earlier this week.
The Home secretary said of the error: "Engineers continue to work to restore data lost as a result of human error during a routine housekeeping process earlier this week.
"I continue to be in regular contact with the team, and working with our policing partners, we will provide an update as soon as we can."