There is nothing wrong with that. That tear is the testimony of the love you had for Pooder, the sensibility of your soul, and your understanding of animals. Don't push it away. These are great qualities and Pooder has been very lucky to have had you in her life.
I know how hard it is. I still miss my Amber girl and it's been just over two years since she's been gone. I've even been known to still slip up and call Jersey "Amber" on accident. Heck, I still get a little teary eyed when I think of the Doberman we had when I was young. He was a very special boy. For most of us, losing a pet means losing a part of our family. And while we move on we never forget them...and personally, I wouldn't want to.