Police put forward “pretty strong views” that there was no need for a report but the ex-Tory leader said the families should have been listened to.
The disaster, which killed 96 Liverpool fans in 1989, is at the centre of the biggest ever inquiry into police wrongdoing in the UK.
Last September a damning report by the Hillsborough Independent Panel found that South Yorkshire Police orchestrated a cover-up, falsified documents and blamed innocent supporters in the aftermath.
The lives of 41 fans could have been saved, the report concluded, as it cleared supporters of any wrongdoing or blame for the disaster.
Sir John said: “The Hillsborough report was pretty shocking. When there was agitation for a Hillsborough report we had pretty strong police views that there was no need for a report at the time and nowadays I’m not sure that assurance would ring as strongly as it did in the 1990s.
“Self-evidently the Hillsborough families who petitioned and demanded an independent report have been proven to be right and we must all say to them we are sorry, we should have dealt with it a good deal earlier and we should have listened a good deal more carefully.
“And I’m very happy to say that to the Hillsborough families today. We should have done more and I’m sorry in retrospect that we didn’t.
“It is one of many things that you can look back on and regret.”