Slugs are a sign of moist areas. While they can feed on lawns, they rarely will feed to the point of causing damage. Any browning would more likely be due to lack of fertility, fungus, or environmental causes. Some browning is not unexpected at this time of year with all of the rain we've received. This can lead to the onset of several disease issues. They typically resolve by the end of the season, and the lawn would benefit from a fall fertilizer application.

If you have a picture of the affected area of your lawn, feel free to include.