You should expect to lose your first two hour game; nobody is ever good at something their first try.
Just played my first 2+hour chess game today and lost.
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Only if you were winning the whole time and totally blew it in the end then it's very normal but it's chess and it happens. It's normal to be bummed out about losing but look at it another way: You just played 2+ hours that means that it was probably a fairly close and mentally intense game. Nothing to be depressed about there; that's actually pretty awesome. Losing just means you have the chance to analyze (if you wrote it down) and learn from your mistakes and improve your game.
I felt depressed afterwards. Is that normal?