Operators of the renovated Nassau Coliseum have responded to complaints about high parking prices by putting a $20 ceiling on parking passes bought online for concerts and special events.

Nassau County’s 2013 lease with operator Brooklyn Sports & Entertainment mandated that the developer provide at least 2,000 of the arena’s 5,800 parking spots at a price not exceeding $20. The lease did not control the parking price once those 2,000 parking passes were sold out.

Many patrons at the Coliseum’s inaugural show by Billy Joel on April 5 expressed sticker shock at the $40 parking fee, with some vowing to boycott future events. Many made their feelings known on social media and in calls to the county and to local legislators.

All Coliseum patrons now will be able to buy parking passes for $20 or less online before shows, according to Brett Yormark, chief executive of Brooklyn Sports. Parking passes bought at the arena on the day of the show still will cost $30 for most concerts and $40 for special events, including Thursday’s Barbra Streisand concert.

Yormark declined to provide a reason for the change. But he said he hopes the new policy will encourage visitors to purchase their parking in advance.

“By expanding the program, not only will guests save on parking, they will enter more efficiently and also help reduce delays for other patrons,” he said. “Those that do not prepay will incur higher parking fees on-site for concerts.”

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Nassau County Executive Edward Mangano took credit for the change, saying it came after he “expressed the frustration felt by our residents” to Brooklyn Sports management.

Democratic Minority Leader Kevan Abrahams (D-Freeport), who urged Mangano last month to renegotiate the parking rate, commended Brooklyn Sports for “listening to frustrated concert goers and putting them before profits.”

Patrons at the arena, known as NYCB Live’s Nassau Veterans Memorial Coliseum, can buy parking passes at nycblive.com/parking or Ticketmaster.com and will be able enter the parking lot through express lanes.

Tickets to family shows, such as WWE wrestling and the Harlem Globetrotters, will cost $5 to $15, whether purchased online or on the day of the show.