The fact that you're running Eclipse is tangental. To work properly, a webapp must be in WAR format, Eclipse or not, and that means that you must have a copy of the JAR in the WAR's WEB-INF/lib directory.
Eclipse normally doesn't automatically do that kind of stuff, which is why tools such as
Ant and Maven are commonly used in webapp development. There are Eclipse plugins for both of these tools (Ant is built-in to the standard
Java distro).