Lord Hutton has described the bill that resulted from his report into public service pensions as "needing improvement".
The Labour peer was speaking during the second reading debate on the Public Service Pensions Bill, on 19 December 2012.
The bill is based on a report by the former Labour minister, who designed four key tests for public service pension reform: affordability, fairness to public service workers, fairness to taxpayers, and transparency.
The bill moves public sector pensions over to a career average scheme and increases the age at which members can draw their pensions.
Speaking during the debate, Lord Hutton told peers the bill would be "fairer" than current public service pension schemes, particularly for low paid workers.
He said: "The final salary schemes that make up the rest of the public service pension schemes are essentially unfair to the people we should be most concerned with - which are those people in the public sector who earn the least.
"It is those people who earn the least in a final salary pension scheme who subsidise the pensions of those who earn the most."
But Lord Hutton wanted it written into the bill that the new pension boards should include employee representation.
He told peers: "We should remind ourselves that in the private sector schemes there is a legal requirement for a third of the trustees to be employee nominations, and I think there is a very strong case for something similar for the pension boards that this bill is going to set up."
Baroness Noakes, a frontbench Treasury spokeswoman when the Conservatives were in opposition, used her contribution to say that the reforms did not go far enough.
She told peers there was "no fairness" in forcing taxpayers to fund schemes that would be unavailable to most people.
Keeping defined benefit pensions for public sector workers was "simply out of line with the rest of the economy", she said.
Treasury spokesman Lord Newby, introducing the bill, told peers: "We must have public service pensions legislation that is fit for purpose - legislation that ensures that those who commit their careers to delivering our valuable public service continue to receive guaranteed benefits in retirement that are amongst the very best available.
"But we also have an obligation to ensure that these generous arrangements are provided on a fair, transparent and sustainable basis."
For Labour, Lord Davies of Oldham said public sector pensions needed to remain "good quality" but also be "affordable".
"We all recognise that this bill is based on sound principles and needs to be supported across the House," he said, although raised a series of details issues he said he would return to during the legislation's passage through the Lords.
The bill received an unopposed second reading and will now proceed to committee stage.