Here's the short of it all:
If you declare war/if you are the aggressor, then your people will complain.
If you are attacked/if you are the defender, then your people will want to fight.
So what happened in your situation:
You attacked the US, you became the aggressor, then the alliance attacked you, you became the defender, this probably balanced out everything. In fact, I think your people may still love you for defending the nation.
Personally, I have never had a significant problem with War Weariness, if anything I've only noticed their love for their defender!
Be the hero, not the tyrant.