Probably, depending on the type of herbs. What kind of soil did you use?
Basil and many other annual herbs, oregano, marjoram lemon grass...they don't mind moisture as much as things like lavender, santolina, rosemary, savories do. If left in el cheapola potting soil (I'm thinking Hyponex) they can stay soggy once soggy and croak.
Other soils should dry out enough over the next few days to keep 'em alive.

Consider adding a course draining "something" to your container next year, or prepping a bed area for your herbs. I amended with manure and chicken grit. My "dry" loving herbs like this. The rest not so much so I plant annuals and more water lovers with the vegetables.

GGG