What is that feeling...?

Solution 1:

Crestfallen
It is to be sad and disappointed in one go.

adjective
1. dejected; dispirited; discouraged.
Dictionary.com

Other options include:

Dejected
sad and depressed

adjective
1. depressed in spirits; disheartened; low-spirited
Dictionary.com

Disappointed
displeased due to a failing in expectations

adjective 1. depressed or discouraged by the failure of one's hopes or expectations
verb
to defeat the fulfillment of (hopes, plans, etc.); thwart; frustrate
Dictionary.com

Solution 2:

In simple words, rejection is what is actually felt. But consider these terms:

Friendzoned (or brotherzoned, in this case)

Although, not a term for the feeling per se, the concept is, in popular culture, referred to as getting friendzoned, where your love for someone is not reciprocated, and instead they say something along the lines of "I consider you as a good friend, and nothing more".

Read about friend zone on Wikipedia, and similar slang expressions on Urban Dictionary.