Owner Andy Lonsdale had promised to invest £1million in the club but he did not arrive at the hearing on time, reportedly claiming he was stuck in traffic.
It was the 10th time Lonsdale had been ordered to appear at the High Court and, despite his barristers saying they had a statement that the money was in the bank, the judge was not satisfied there were sufficient funds.
The winding-up petition was brought by HM Revenue and Customs, one of the club's creditors.
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It brings to an end a sorry saga for a club founded in 1924 and most famous for knocking Newcastle out of the FA Cup as a Southern League club in 1972.
Hereford were elected to the Football League following that triumph and spent 31 seasons in the league in two spells before relegation to the Conference in 2012.
This summer they were expelled from the Conference for financial irregularities and began this season in the Southern League Premier Division.
Martin Watson, vice-chairman of the Hereford United Supporters' Trust, told BBC Hereford and Worcester: "It's the end of something I've been a fan of for 30 years. It hurts but it had to be.
"We never thought we'd come to this. We were promised so much over the last few months and nothing was delivered.
"Hereford United will continue because we, the fans, are Hereford United. We'll think about it, we'll take a moment, then we'll pick the pieces up and start again."
Herefordshire Council, which owns Edgar Street, is seeking repossession of the ground as soon as possible.
In a statement, the council said: "As Hereford United Football Club (1939) Limited is in the process of being wound up and a liquidator will be appointed, this action triggers the council's right as landlord to forfeit the leases.
"The council will now pursue this and seek to gain formal repossession of all three sites leased to the club.
"Once the ground has been secured, the council will consider the appropriate process for procuring a new tenant to ensure the continuation of football.
"The council is unable to seek immediate possession of the ground, there is a prescribed legal process which the council must adhere to. At this point in time we understand that this process is likely to take a couple weeks."
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