The National Audit Office (NAO) report said the Big Lottery Fund (BLF) failed to challenge Big Society Network's (BSN) "ambitious" target for recruitment of members to the Your Square Mile project before handing over the money, even though meeting the numbers was key to its success.
The finding was one of a number of criticisms relating to grants totalling more than £2 million to projects linked to the BSN and its charitable arm the Society Network Foundation.
The Big Society Network was launched by David Cameron at 10 Downing Street two months after winning power in 2010, with the aim of encouraging community work and volunteering.
Within months of the Network's creation, the Big Lottery Fund asked it to submit a bid for a grant to fund the Your Square Mile project, which was intended to encourage work in the community through a website, mobile phones and public access screens.
The NAO found the process of soliciting the application was in line with BLF procedures, but the Fund did not challenge recruitment targets, and then allowed the grant to be transferred to a new company Your Square Mile Ltd (YSM), set up by the BSN chairman and another director, without checking it had the IT skills to make the scheme work.
By October 2011, the Fund judged successful completion of the project was "unlikely".
By the end of its first year in February 2012, rather than one million members, whose subscriptions were needed to fund operations, YSM had recruited just 64.
The Big Lottery Fund said in a statement: "We are grateful to the NAO for their work on this report and are pleased that it finds these grants were awarded in line with the Big Lottery Fund's procedures for soliciting and assessing bids and that the fund followed its standard approach in doing so.
"As a funder we are committed to supporting riskier projects on occasion, and not just the tried and tested.
"It is in the nature of such projects that sometimes they don't achieve their intended outcomes."
A Cabinet Office spokesman said: "We are backing organisations which encourage people to volunteer and use their talents.
"Society Network Foundation won a grant to deliver such a programme, but despite their efforts and our support, it was unable to make it work and so we ended our funding.
"Trying new things and being innovative means taking sensible risks.
"The mistake is not trying something new it is to keep doing something that has been shown not to work."