The funding body has also refused to budge from its decision to cut all funds from Paralympics sports goalball, visually-impaired football and wheelchair fencing.
UK Sport insists its funding system has been proven to work in terms of winning medals. It did however reinstate money totalling £894,000 for women's weightlifting in the run-up to Rio 2016, while badminton has been awarded an extra £250,000.
Loading article content
British Swimming called it "a very dark day for British sport" while basketball called for a change in the funding system to treat team sports differently.
David Sparkes, the British Swimming chief executive, called on sports minister Helen Grant to intervene, but there was no response from her office. "This is a very dark and sad day for British sport, especially for women's sport," he said.
"On behalf of water polo, synchro and other Olympic sports that face the real possibility of dying out as a result of today's announcement, we call on the sports minister to show leadership by looking at the entire funding system for elite sport."
Sparkes said the decision on synchronised swimming "beggars belief" and "highlights a fundamental flaw in the UK Sport funding system".
British Basketball will also consider making a formal appeal and it too called for political leadership to find a solution to an apparent funding gap affecting team sports. Countries such as Canada have adopted different funding systems for team sports and individual sports.
Roger Moreland, the sport's performance chairman, said: "Winning medals now and in the future should be celebrated, but we need to consider its impact. Basketball has a grassroots base bigger than any other British Olympic team sport.
"A funding system with nearly £350m available for elite sport cannot be working to the best of its ability, if it can leave sports like basketball behind.
"If there is the political will and the leadership, a solution can be found. Other countries have done so."
UK Sport chairman Rod Carr said to fund basketball would see £33m being spent on the sport between 2006 and its first likely medal chance in 2024.
He added: "To invest £33m at that rate is frankly not a good use of public money.
"Basketball is 22nd [in the world] at the moment that is a long way from its target of sixth to eighth at Rio.
Carr said made a differentiation between team sports and other sports was "a difficult area" and said the 'no compromise' approach targeting funding to medals had been proven again to work at the Sochi winter Olympics and Paralympics.
He added: "We can't actually see why there should be that criteria. We would be saying team sports are more important than other sports.
"I accept that by its very nature 'no compromise' is not universally popular but there's one thing we are sure of - it works."
UK Sport also pointed out that basketball received £10.5m from Sport England for its grass-roots programmes and that providing money to help its development would affect medal chances in other sports.