Simon Hughes told a Lib Dem conference event in Brighton last night that the plan was blocked by civil servants, by universities and by fears any delay in legislation would lengthen student protests.
At the event on the future of universities, hosted by the Social Market Foundation and Universities UK, Mr Hughes looked back to events following the publication of the Browne Review of higher education funding in October 2010.
He said the Lib Dems "would not have had such a difficult ride at all had we persuaded the civil servants and our coalition colleagues of something that I think we could have persuaded them of...and that is that we could have voted to get rid of tuition fees by repealing that piece of legislation and introduce a short piece of legislation - and that's a graduate contribution system."
Mr Hughes said the proposed graduate contribution system "was a very short distance away from the [National Union of Students] position".
Looking at why the proposed policy "unscrambled", he said that "universities, in particular, backed by the civil servants, said...'It can't wait any longer, we need to know what the fees are going to be'".
Mr Hughes said universities' fears at the time over the urgent need to include 2012/13 fees in prospectuses were "not necessary", as the legislation for a graduate contribution system could have been in place by January or February 2011.
He added of the longer process needed for graduate contribution legislation: "The government business managers...they were unnerved that we could have had not just one big day of student demonstrations...but two weeks of it, getting nearer to the elections in the spring of 2011."
But Mr Hughes said: "Had we done it that way in the end we [the Lib Dems] would have had much less flak, the government would have had much less flak, students would have been much less angry, and we would still have addressed the question of how you get more money into the system for higher education at a time of economic difficulty."
Nicola Dandridge, chief executive of UUK, told the event that UUK believed the coalition "did the right thing" by increasing the fee cap.
The Liberal Democrats "should be admired" for their stance on fees, she added, and the sector owed Nick Clegg, the deputy prime minister, and Vince Cable, the business secretary, "a debt of gratitude".