In this sentence, we're dealing with a conditional statement. The first part ("If it had rained, we would have had to postpone the concert") sets up a hypothetical situation in the past. It describes what would have happened if a certain condition (rain) had been met. The second part of the sentence ("It didn't rain") indicates that the condition was not met. Since it didn't rain, the hypothetical scenario described in the first part didn't actually occur. So, we need to choose an option that conveys that no action was necessary because the condition (rain) didn't happen. "We didn't have to" fits this context perfectly because it means there was no obligation or necessity to postpone the concert since it didn't rain.