DI is not supported for any kind of application class in a J2EE 5 application.
http://forums.oracle.com/forums/thread.jspa?threadID=447310
If you have a look at the J2EE 5 spec, the classes where DI is supported are listed on page 64.
Component classes supporting injection
Servlet: servlets, servlet filters, event listeners
JSP: tag handlers, tag library event listeners
JSF: scoped managed beans
JAX-WS: service endpoints, handlers
EJB: beans, interceptors
Java EE platform: main class (static), login callback handler
So if you want to use DI from a JSF scope managed bean, it must be supported.
Robin