I grew up near a ton of pecan trees and they would get infestations of web worms every few years. they aren't all that harmful, other than eating some leaves.
Many ways to get rid of them without using pesticides or chemicals and they are just as, if not more effective. You did one of those methods - removing and discarding. Others include soap and water like described above. Another soap method for shorter plants is to take a bucket of soapy water and dip the webs in the soapy water. Drowns the worms.
The most fun is to tear the webs open with a stick and let the birds at them. Once a few birds know about it, others will arrive.