At the restaurant I use a burgundy blend that's made specifically for cooking. At home, I like to use red table wine that comes in glass jugs. What you're really looking for is a wine that isn't noticeably tannic or acidic. As the wine reduces down, these flavors will concentrate and effect the overall flavor of your sauce.

Pan sauces are rarely strained only because they're usually made a la minute. You could do something on a larger scale just like the pan sauce, strain it through a chinois into a sauce pot and mount with butter and lemon right before serving.

The reason for straining a pan sauce is purely textural. By the time my stock is ready to be used for a pan sauce, it's been reduced, reinforced and strained quite a few times.

I happen to like the roasted shallots in my pan sauce. If you don't want that extra textural element, you can strain before serving.

@Teixierat,

What type of stock are you using? Are you making your own or using store bought? It sounds like your stock doesn't shave enough gelatin in it.

Also, when you add in the butter, you want to do it over low heat and then turn the heat off right before the butter is completely melted into the pan sauce, swirling or whisking constantly. However, if your sauce doesn't thicken properly before you add the butter, then it's extremely hard to keep the butter emulsified in the first place.

If you don't have a good stock with gelatin, then you need to reduce your wine until it's almost dry, and then mount with butter. But then at that point you'd be making more of a beurre blanc.

Yes, the bitterness could have come from the wine. This happens if the wine is a little acidic or tannic to start with. Also, at any point in the reduction process, if you happened to "scorch" either your stock, wine or shallots, that could also have contributed to the off flavor.