Draper has been in charge of British tennis since February 2006
The Lawn Tennis Association's image has been hurt by a lack of transparency over its spending, the All-Party Tennis Group has warned.
In a carefully-worded letter to Sports Minister Gerry Sutcliffe, Baroness Angela Billingham said "esteem for the LTA seems to be at an all-time low".
Billingham said this means the LTA does not always get the credit it deserves.
This will come as some relief to under-fire LTA boss Roger Draper but the group's overall message was critical.
"The LTA is attempting a host of initiatives which have complex social dimensions," Billingham, the All Party Tennis Group's chair, concluded.
"But given the remarkable level of expenditure, in excess of £60m annually, it should be possible to deliver better outcomes than at present."
The group's report comes after a miserable month for British tennis which started with a fifth straight Davis Cup defeat - to lowly Lithuania - and ended with a second consecutive early exit for Andy Murray in the US.
The perception of tennis as a middle-class sport has to be countered by high-profile initiatives to make it a sport for all
Baroness Angela Billingham
Chair of All Party Tennis Group
That Davis Cup humiliation saw the end of John Lloyd's stint as GB captain and prompted an internal review of British men's tennis.
But more significantly, it also heralded a public debate about Draper's four-year tenure at the national governing body.
Much of this debate has been conducted in the media but it also fed into the deliberations of Billingham's panel, which heard evidence from the likes of Tennis for Free advocate Tony Hawks and former Murray coach Mark Petchey from one camp, and Draper from the other.
The BBC understands Draper put up a vigorous defence of the LTA's spending and denied there was a profligate "bonus culture" at the governing body.
He also pointed out he was only four years in to his 10-year plan to revitalise British tennis and some progress had been made.
The All Party Tennis Group, a cross-bench panel drawn from the Lords and Commons Tennis Club, acknowledged Draper's points about the positive steps taken in some areas but this was not an unequivocal endorsement.
Billingham's letter makes it clear the panel, which is only an advisory body, believes the LTA should focus more of its resources on the mass participation side of the sport than it currently does.
"The public perception of tennis as a middle-class sport has to be countered by high-profile initiatives to make it a sport for all," she said.
As well as the veiled criticism of the LTA's "priorities", the All Party group also called upon Draper's organisation to be more "transparent and accountable" about its targets and how it spends its money.
On this last point Billingham suggested Sport England, the government agency that distributes public money for grassroots sport, should accept more responsibility for the £26.8m tennis has been given over four years.
"In particular, care should be taken to ensure the bonuses paid to LTA staff are in clear recognition of quantifiable success in performance," she added.
The LTA responded to Billingham's letter by welcoming the All Party Tennis Group's offer of help in communicating the good work it does and reiterated its commitment to providing "accessible, affordable tennis".
In an official statement, the LTA said it was also happy to explain how it uses its public funding "at any stage" and denied any Sport England money had gone into the payment of bonuses.
Sport England agreed with the All Party Group's calls for greater transparency and said it would be publishing a first annual review of the LTA's activities in the autumn.
The funding agency's chief executive Jennie Price told BBC Sport that it had agreed "clear milestones" with the LTA and could say "to the penny" how Sport England's money is being spent.
"We have made clear to the sports we fund that our support is an investment, not a donation, and that they must regularly demonstrate to us how they contribute to getting more people playing and enjoying sport," she added.