Hey die_nerd,
There is currently a bug where if your emblem slots are full you will not receive the exotic "Eye of Osiris" emblem. The current solution is to complete it again on another character and receive the emblem with open inventory space.
I'm sorry that you lost it :( I believe Bungie is aware of the issue.
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Ugh, I really do not want to spend another few hours completing this. I have already spent hours on hours attempting to complete this and I really feel that I deserve the emblem... I really wish this wasn't a thing.
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It is a nasty glitch. You'll be able to get it next week, when the Trials, on your main character. Until the issue is resolved, keep at least one inventory slot open for rewards.