You said something you didn't intend to Your phrasing there means something else You're not saying what you want to That's not what you want to say (to convey that) That means something different from what you think You're not getting across the idea/meaning/what you want to

Use "than" rather than "from". Your words came across differently than what you were trying to say. OR Your words came across differently than you thought.

That all looks good. "Your words came across differently from what you were trying to say, because of the grammar (or "grammatical") mistakes you made." (You don't really need "in the sentence".)