Neighbor’s insurance just offered far less than the damages incurred, what should I do?

Out upstairs neighbor’s hot water heater blew up and ruined our furnace and caused other damage. The furnace replacement alone was $6800. The mitigation was several thousand more. Their insurance company offered about $5800. What should I do? Is suing my neighbor in small claims court the best option? It seems like even if their insurance offers us more it won’t be enough to cover all of the expenses we incurred. It’s pretty disappointing, their property damaged our property, why should it cost us anything to have it fixed? Doesn’t make any sense to me and I would love some insight. Thank you