The government has previously said the cull of badgers is necessary as part of a "science-led" programme to tackle TB - which has been devastating to farmers.
The first minister said that the decision was "disappointing" and stressed that bovine TB was a "serious problem for the milk industry in Wales and had led to the culling of thousands of cattle in recent years".
The Conservatives' election manifesto had promised to "introduce a carefully managed and science-led policy of badger control in areas with high and persistent levels of bovine TB".