No you are fine. This is part of what they are. They have terrier in them. If you were walking a rat terrier it would do the exact same thing. Its in their genes to go after small creatures. Terriers were bred for this job and it is part of your pit as well. Also they arent vampires they arent going to taste blood then suddenly want to go kill everything in site. LOL =) My pit does the same i just hold her leash tight and keep walking and she forgets about them.