The Loudoun County Board of Supervisors voted Wednesday to adopt a $1.8 billion budget for fiscal 2014, a plan that will lower property taxes for most county homeowners but leave the public school system facing a $15 million shortfall.

The board voted to set the county’s real property tax rate at $1.205 per $100 of assessed value, a decrease of 3 cents from the current property tax rate of $1.235. At the new rate, a resident with a home assessed at $405,000, the current average value, could expect an annual property tax reduction of about $69, according to county staff members.

The board also voted to adopt a capital improvements program of $1.73 billion to fund government and public school projects through 2018. Transportation was the largest funding category in the program, which includes $124 million for road, trail and sidewalk projects across the county.

Adoption of the budget followed a series of public input hearings at which scores of speakers urged the board to fully fund the School Board’s requested $859.7 million spending plan. Despite residents’ appeals, the plan approved Wednesday allots $841.7 million for public schools, leaving an $18 million funding gap. Additional state funding is expected to reduce the shortfall to about $15 million.

Many residents urged the board not to “cut” the School Board budget during the public input sessions, a word that prompted sharp responses from some supervisors who emphasized that the county board has consistently boosted funding for the rapidly growing school system. The plan adopted Wednesday increases the School Board’s funding by $20.5 million over the current budget.

Throughout the budget process, supervisors have urged the School Board to consider additional measures that would reduce costs, including closing smaller schools, changing retirement and benefit plans for current employees, and working with the county government’s reform commission to streamline functions with the county.

But School Board members have maintained that the requested budget was already lean. Before forwarding the plan to supervisors, the School Board cut nearly $17 million from the $876.4 million budget initially proposed by School Superintendent Edgar B. Hatrick III in December. The original plan allowed for no new programs, Hatrick said, and represented the minimum amount needed to open two elementary schools and accommodate more than 2,000 new students.

Supervisors have repeatedly expressed disappointment at what they’ve described as unwillingness from the school administration to cooperate with the government reform commission. Those frustrations were echoed Wednesday.

Supervisor Suzanne Volpe (R-Algonkian), who has consistently pushed for deeper cuts to the budget, said she thinks that more could have been done.

“It’s very disappointing, for example, that the government reform commission has not been able to effectively work with the School Board and school administration,” she said. “I believe we were elected to lower the tax burden on folks, and I want to honor my word.”

Supervisor Ralph Buona (R-Ashburn) agreed. “The real issue comes down to did we do enough, and in my own view, we tried. We really tried,” he said. “But I think a lack of cooperation with the reform commission didn’t let us get as far as we wanted to.”

Supervisor Matt Letourneau (R-Dulles) said the budget represented a compromise. Many residents had hoped for a lower property tax rate, “but we’ve also heard from quite a few residents, actually, who wish it were higher,” he said, referring to the numerous residents who pleaded with the supervisors to fully fund the School Board’s budget.

Letourneau said that he had concerns about how the schools might manage but that, overall, he was pleased with the budget.

“I think it’s a good work product and something we should be proud of and support,” he said.

The budget, tax rate and capital improvement program were adopted in a series of split votes. Board Chairman Scott K. York (R-At Large), Vice Chairman Shawn Williams (R-Broad Run) and supervisors Geary Higgins (R-Catoctin) and Letourneau voted in favor of all budget motions. Supervisors Volpe and Eugene A. Delgaudio (R-Sterling) voted against all aspects of the budget.

Supervisors Kenneth D. Reid (R-Leesburg) and Buona were divided in their votes. Reid supported the amended budget but voted against the proposed tax rates and the capital improvement program. Buona abstained from the vote on the tax rate, voted against the amended budget and supported the capital improvements.

Supervisor Janet Clarke (R-Blue Ridge) was absent from the meeting because of a death in her family.