The two projects are among five state-of-the-art sports centres that were to be built in NI in the countdown to the 2012 Olympics.
All five have now been shelved after a £50m Government budget cut.
Also included in the cuts are a cycling velodrome and a sailing facility with the Stormont Sports Minister saying cuts meant the money was no longer there for them.
The DUP's Nelson McCausland added that none of the projects had yet produced a "satisfactory business case".
"With all of them, when they were scrutinised by Sport NI and by the economists internally it became clear that there were significant issues that needed to be reviewed," Mr McCausland said.
He added: "I fought very hard for sport in our capital programme and over the next four years we will have £130m of capital spend on sports infrastructure in Northern Ireland."
However, he said: "There are a range of competing interests and competing demands."
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In response, the Lagan Valley Alliance Chair Stephen Martin expressed his disappointment at the Department of Culture Arts and Leisure's decision to cancel their backing of a proposed new basketball centre of excellence in Lisburn and tennis facility at Hillsborough.
Stephen Martin said: "This is a bad day for local sport and I am disappointed at this news.
"This is a challenging economic time and government both at Stormont and at local level are trying to ensure that taxpayers money is essentially diverted to protect vital frontline services. The very sad consequence is the loss of exciting projects like these.
"I am disappointed that we have lost out on funding for a new basketball centre of excellence due to be based in Lisburn and also with a tennis facility in Hillsborough.
"These projects are investments in our future especially those of our city's young people. Sport is the most important outlet for kids and ensures that they have a focus to help combat potentially negative influences. Money spent now ensuring kids are active and healthy will save us all in the long run," he said.
The Ulster Unionist Councillor David Archer has also expressed his extreme disappointment and frustration at the decision to withdraw funding for the proposed Elite Basketball facility at the Laurelhill Sports Zone and the elite Tennis centre at Hillsborough.
Councillor Archer, who represents Lisburn Town North said: "This announcement is just the latest blow to the city of Lisburn and the wider Lagan Valley Constituency, which has already suffered from the collapse of the National Stadium project and the prevarication over the John Lewis development.
"Lisburn - or more specifically Laurelhill Sports Zone - had been identified as the site of one of the five prioritised Elite Facilities for the London Olympics 2012, where Lisburn City Council was in partnership with Ulster Basketball, Northern Ireland Volleyball, Knights Wheelchair Basketball, Laurelhill Community College and the SEELB.
"The Borough also had high hopes for the elite Tennis centre at Hillsborough.
"For these projects to be pulled at this late stage, bearing in mind the amount of work and money expended on it already, is little short of scandalous," he fumed.
(BMcC/GK)
