June 21 (Reuters) - The record demand for a Federal Reserve program that lets money market funds and other firms park cash with the Federal Reserve overnight is not concerning and the tool is working as intended to help set a floor on short-term rates, New York Fed President John Williams said on Monday. "It"s effective and I"m not concerned about the amount of uptake on that ... or whether it would increase further," Williams told reporters. "It would just be a sign that it"s working as planned." Usage of the program, known as the reverse repo facility, surged further after the Fed lifted the rate it pays firms to 0.05% from zero at last week"s policy meeting, a move Williams said was aimed at helping to keep the Fed"s key benchmark rate within the target range of zero to 0.25%. Firms parked a record $765 billion overnight with the Fed on Monday.