The PM was speaking after an independent report into previously unseen documents showed police had not done enough to stop the disaster.
In 2004, Mr Johnson was at the centre of a storm over an article saying "drunken fans" were partly to blame.
He subsequently apologised to victims' families during a visit to Liverpool.
An editorial in 2004 in the Spectator magazine - which Mr Johnson then edited - accused Liverpudlians of "wallowing" in their "victim status" over Hillsborough and the death of Iraq hostage Ken Bigley.
During exchanges in the Commons after the report's release, Labour MP Yasmin Qureshi urged the prime minister to demand an apology from the London mayor.
She told MPs: "Whilst I accept that politicians cannot make the emergency services and public officials apologise... perhaps the prime minister could ask the mayor of London for an apology for derogatory comments he made about the people of Merseyside many years ago as a result of the Hillsborough disaster."
Mr Cameron replied: "First of all, on what the mayor of London or others have said, I think this report is important because, as I have said, people right across the country, whether they are in positions of power and influence or not, this now is the proper explanation of what happened and people who thought it was something else need to come to their senses and realise this is what happened."
The PM has said he is "profoundly sorry" for what he called the double injustice of the Hillsborough disaster.
Mr Johnson, who was a Conservative MP in 2004, has not commented since the report was published. But ahead of publication he told London radio station LBC that he was thinking of the Hillsborough families and had no more to add to his 2004 apology.
The original, unsigned, Spectator editorial said: "The deaths of more than 50 Liverpool football supporters at Hillsborough in 1989 was undeniably a greater tragedy than the single death, however horrible, of Mr Bigley; but that is no excuse for Liverpool's failure to acknowledge, even to this day, the part played in the disaster by drunken fans at the back of the crowd who mindlessly tried to fight their way into the ground that Saturday afternoon.
"The police became a convenient scapegoat, and the Sun newspaper a whipping-boy for daring, albeit in a tasteless fashion, to hint at the wider causes of the incident..."
After his visit to Liverpool Mr Johnson wrote in the Spectator: "It was sloppy to repeat the old canard that the Hillsborough tragedy was caused by drunken fans, when the inquiry report found no evidence for this whatever.
"To judge by the huge mail I have received, that mistake caused real offence and hurt. Faced with such anger, any editor would feel obliged to make amends, and that is what I do now."