This came after Labour councillors succeeded in watering down the motion with an amendment stripping out the binding commitment.
Lib Dem councillors voted against the Labour amendment and were supported by the Merton Park Independents.
The Conservative councillors refused to join the Lib Dems in voting against the amendment, instead choosing to abstain.
The Conservative group then abstained again on the final motion.
Speaking after the meeting, Cllr Paul Kohler, the Lib Dem parliamentary candidate for Wimbledon, said: “Last night’s motion was an opportunity to ensure the Council enforced the covenants to prevent the All England Club concreting over acres of Wimbledon Park.
“Sadly, that opportunity has been lost due to Labour evasiveness and Conservative inaction.
“I am surprised and hugely disappointed by the Conservative councillors’ refusal to back our proposal last night.
“Despite arguing in favour of the substance of our motion, they refused to join us in voting against Labour’s cynical amendment that stripped out the binding commitment requiring the Council to enforce the covenants.
“They then failed to vote on the final motion, choosing to abstain again. I am not sure why they bothered to turn up as they simply sat on their hands.”
“Conservative councillors might claim they want to save Wimbledon Park, but actions speak louder than words.
“The Conservative group’s preference for playing politics over making real progress has set our campaign back. Wimbledon residents deserve far better from their elected representatives.
“Despite the events of last night, the battle is far from over.
“We have at least succeeded in getting a commitment from the Council to “respect” the covenants, and I and my Liberal Democrat colleagues will continue to campaign to ensure these covenants are enforced and the All England Club’s over-development blocked.”