This sounds like sawfly damage aka rose slug, which isn't actually a slug or a caterpillar. The are tiny green wormy looking creatures are the larval form of the sawfly found on the underside of the leaf . You can either squish them or hose them off with a hard spray of water. Insecticides work, but why bother when water does as well. The key is to get them when you first notice the damage and keep at it until you don't find any more. If they are in pots, covering the soil with landscape fabric can keep them from pupating in the soil and returning for round two!