Robertson was a key figure in the country's doomed attempt last year to bring the tournament to the country for the first time since 1966.
He acknowledged the Government and Football Association had shown "naivety" in believing the empty promises of FIFA executive committee members to vote for England.
Speaking a the Leaders in Football conference in London, Roberston said: "When I look back on my 18 months as a minister, the single greatest failure was our inability to win that bid."
England's failed attempt coincided with the corruption scandals that dogged the world game's governing body last year.
FIFA president Sepp Blatter is due to announce this month a series of reforms aimed at ensuring greater transparency within the organisation.
Some have cast doubt on how effective these measures would be.
Insisting he had no personal animosity towards Blatter, Robertson said: "He will be judged over whether those reform proposals are deliverable."
Robertson is at the heart of attempts to shake up the running of the domestic game and revealed the Government had already begun to draw up legislation to impose on English football if it failed to heed their call for change.
The coalition will this month publish their response to the recommendations of the parliamentary inquiry into football governance, and although they do not want to legislate, Robertson said they would if necessary.
Indeed, the Sports Minister warned that could involve all the Department of Culture, Media and Sport Select Committee's recommendations being imposed, even though he admitted their report contained "some shortcomings".
Speaking at the Leaders in Football conference in London, Robertson was confident the Football Association, Premier League and Football League would get their own houses in order.
But he said: "If that process stalls, and only if it does, then the Government will bring forward legislation, but it will be on the basis of that select committee report."
He added: "We're in the process of drawing up the legislation just in case that becomes necessary.
"I really hope it won't be.
"If something gets imposed from parliament, it will be quite difficult for me to hold the line over what is reasonable and what is not."
Robertson revealed the Government's response would include setting the FA, Premier League and Football League a timetable to address three key issues from the inquiry - those being the reform of the FA board, the reform of the relationship between the FA board and their council, and the implementation of a licensing system overseen by the FA.