They were promised an all-weather training pitch when the original plans for the development were drawn up.
Children and local sports clubs would have used the pitch but now the area will be covered in concrete after councillors voted to build 25 extra homes on the site instead.
Cllr Stephen Gorys said: "This is a real loss to the whole district.
"A sum of money was set aside for the all-weather pitch but that has slowly eroded and now there is not enough money to build it.
"The developer was offering us about £100,000 whereas they will be getting millions of pounds worth of extra housing.
"The measly £100,000 we've been given is simply not enough.
"It means we've lost yet another important leisure facility in the district, which is disgraceful."
Cllr Gorys added: "They index-linked the amount for the all-weather pitch but never went for a realistic figure in the first place.
"It was under-funded right from the start.
"Now they want to squeeze more and more houses on the site.
"We should be calling for adequate compensation for the facilities we were promised but will now not get."
Independent Cllr Gorys said he told the development control committee it should be pushing the developer for far more but he got "very little support from the ruling party".
"We should not be dismissed out of hand by the developer," he said.
Cllr Carol Leversha added: "I was bitterly disappointed at the loss of the all-weather pitch site at Elvetham Heath, which I had tried very hard to prevent over the past 18 months.
"However, I had to bow to the officers' recommendation that, with the costs escalating to £500,000 plus to provide this facility, and with only £108,000 left from the developers' contributions to fund it, it was a non-starter.
"However, I remain committed to Hart having an all-weather pitch and I will ensure that the lessons learnt from this are not forgotten for the future."
Ron Percival, Hart Council's planning chief, said: "We were looking for an increase in density of development overall at Elvetham Heath.
"The all-weather pitch was part of a package that we didn't have sufficient funds to complete.
"Instead the remaining money will be used to build a footbridge over the railway line and to complete the sports pavilion on the estate.
"We negotiated a sum for the all-weather pitch way back in 1993 as part of a package that included sports pitches, tennis courts and a hard surface play area.
"The amount was index-linked but most of the facilities have cost us more than we anticipated, irrespective of the index-linking.
"Due to rising standards in expectations there just weren't the funds there.
"Our current estimate for an all weather pitch is in excess of £500,000 whereas we only had about £100,000 left within the original agreement.
"However, we haven't abandoned plans for an all-weather pitch elsewhere in the area. It's still something we are looking at but at the moment we have no planning permission for one."