'also' in a negative sentence (a mistake?)

To native speakers of English,

Would you consider it a mistake to use 'also' in a negative sentence?

ex. I also don't think that they are going to win, .... etc.

As far as I can see, 'either' should be used in negative sentences.

Thanks for your comments.

If someone says "I don't think they'll win.", and you say "I also don't think they'll win." , it's perfectly correct, just a little...tight... It's kind of too correct. It's probably preferred to say "I don't think they'll win either.". As far as english goes saying "I also don't..." would be accepted since almost everything goes. Thing is, it's like, how we're told not to end a sentence with a preposition. That's technically false grammar. But we ALL do it. When I hear someone re-wording their sentence so as not to end it with a preposition("about what are you talking."), they just seem overly correct, at this point that phrase is much worse than just saying "what are you talking about". So, not a mistake grammatically, but pretty much a mistake in reality.

Thanks for the insight xX, useful and helpful!