Sure, you can feel lonely for a number of different reasons. Broadly speaking, loneliness is a negative emotional response to isolation (note: "a" negative emotional response, not "the only" response). Isolation can result from an inability to communicate with loved ones, or from not having loved ones with whom to communicate. It's typical of lonely people to seek out meaningful connections and to experience sadness until meaningful connections are found. The OP sought out meaningful connections, was denied, and felt sadness as a result.