How do I inject an event into a servlet in JavaEE7?

Question

I have a @ServerEndpoint that adds web socket sessions and I want it to @Observes an event that will be fired by a servlet and then broadcast a message to all the web sockets.

I get a NullPointerException in my servlet when I try to use the event that was defined with @Inject. What am i doing wrong?

WebSocket Handler:

    import javax.ejb.Asynchronous;
    import javax.enterprise.event.Observes;
    import javax.enterprise.inject.Any;
    import javax.websocket.*;
    import javax.websocket.server.ServerEndpoint;
    import java.util.Collections;
    import java.util.HashSet;
    import java.util.Set;

    @ServerEndpoint("/events")
    public class WebSocketHandler
    {
        //This holds our sessions for async retrieval
        private static final Set<Session> sessions = Collections.synchronizedSet( new HashSet<Session>() );

        @OnOpen
        public void open(Session session)
        {
            //Add to our collection
            sessions.add( session );
        }

        @OnClose
        public void close(Session session, CloseReason closeReason)
        {
            //Just remove it
            sessions.remove( session );
        }

        ...elided...

        @Asynchronous
        public void notify(@Observes @Any TestEvent event)
        {
            synchronized( sessions )
            {
                //Loop through and send to all listeners
                for ( Session session : sessions )
                {
                    //Make sure it's still open
                    if ( session.isOpen() )
                    {
                        try
                        {
                            session.getBasicRemote().sendText( event.getMessage() );
                        }
                        catch (Exception e)
                        {
                            e.printStackTrace();
                        }
                    }
                }
            }
        }
    }

Event type:

    import java.io.Serializable;

    public class TestEvent implements Serializable
    {
        private String message;

        public TestEvent()
        {
        }

        public TestEvent(String message)
        {
            this.message = message;
        }

        public void setMessage(String message)
        {
            this.message = message;
        }

        public String getMessage()
        {
            return message;
        }

        @Override
        public String toString()
        {
            return "TestEvent: " + message;
        }
    }

Servlet:

    import javax.ejb.Asynchronous;
    import javax.enterprise.event.Event;
    import javax.inject.Inject;
    import javax.servlet.ServletException;
    import javax.servlet.annotation.WebServlet;
    import javax.servlet.http.HttpServlet;
    import javax.servlet.http.HttpServletRequest;
    import javax.servlet.http.HttpServletResponse;
    import java.io.IOException;

    @WebServlet("/broadcast")
    public class SendMessageServlet extends HttpServlet
    {
        @Inject
        Event<TestEvent> testEvent;

        @Override
        protected void doGet(HttpServletRequest req, HttpServletResponse resp) throws ServletException, IOException
        {
            //Fire the event (THIS "testEvent" IS NULL)
            testEvent.fire( new TestEvent( "{\"message\":\"An event occurred at " + System.currentTimeMillis() + "\",\"status\":200}" ) );
        }
    }

beans.xml:

    <?xml version="1.0" encoding="UTF-8"?>
    <beans xmlns="http://java.sun.com/xml/ns/javaee"
        xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
        xsi:schemaLocation="
        http://java.sun.com/xml/ns/javaee
        http://java.sun.com/xml/ns/javaee/beans_1_0.xsd">
    </beans>

pom.xml:

    <?xml version="1.0" encoding="UTF-8"?>
    <project xmlns="http://maven.apache.org/POM/4.0.0"
            xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
            xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
        <modelVersion>4.0.0</modelVersion>

        <groupId>groupId</groupId>
        <artifactId>TestWebSocket</artifactId>
        <version>1.0</version>

        <packaging>war</packaging>

        <!-- Tell Maven what language version to use -->
        <properties>
            <maven.compiler.source>1.8</maven.compiler.source>
            <maven.compiler.target>1.8</maven.compiler.target>
        </properties>

        <dependencies>

            <!-- Enables the annotations, etc needed -->
            <dependency>
                <groupId>javax</groupId>
                <artifactId>javaee-api</artifactId>
                <version>7.0</version>
            </dependency>

        </dependencies>

    </project>