For New York City’s luxury real estate brokers, a new mansion tax certainly isn’t welcome news, but it’s better than the alternative.

The tax, included in the new state budget and replacing an annual pied-a-terre levy, would be a one-time payment that’s less likely to scare buyers away, brokers say. It’s just the entry fee into New York’s exclusive market.

“We probably dodged a bullet here,” Steven James, chief executive officer of Douglas Elliman’s New York City division, said in an interview. “It’s not the catastrophe we thought was going to happen.”

New York’s powerful real estate industry succeeded in...