Councillors in the Calverley & Farsley ward have been left "absolutely furious" with the delay in moving travellers from Woodhall playing fields.
The travellers arrived at the site off Woodhall Lane, Calverley, last week.
Councillor Amanda Carter said council tax payers will be left to pick up the bill following a delay in moving them on.
Councillor Amanda Carter said: “We asked the Council, right at the beginning, to serve what is known as a Section 61 Notice or rather ask the Police to.
"Apparently without the Council asking the Police the Police are left powerless. This is a nonsensical situation.
"Residents are rightly angry and it is going to be us, the council tax payers, left to pick up the bill.”
Councillor Andrew Carter said the problem goes "right to the top and the council’s senior management team and the Labour administration".
The councillor added: "I feel sorry for the council officers on a day to day level who are now left to clear up this appalling mess.
"Pitches that were being prepared for the football season are now unplayable.
"How can this not have been priority land?
"At the very top of the Council there has been a complete lack of urgency leaving council officers further down the line frustrated and facing a clean up and Councillor Amanda Carter and myself absolutely furious.
"It is simply not good enough."
A Leeds City Council spokesperson said: “We treat every unauthorised traveller encampment very seriously.
"In some circumstances, the police are able to use a Section 61 notice to require a group to move.
"In this particular instance, the police have not used their powers because the conditions have not been met.
"In terms of the action that the council can take, it requires a court order to remove the encampments, which we have now obtained to reclaim possession of Woodhall playing fields.
"Once the encampment has fully left, we will be undertaking a full clean-up of the site.”