Did Brian actually tell Julie that she was a F*** buddy?

In the party when David meets Sofia, there are a few quick shots of Brian trying to talk with other women, until he gets into a conversation with Julie. Brian is very drunk and somewhat angry that David had already stolen Sofia's attention, and it is implied that Brian (maybe unintentionally) told Julie (his crush) about her being David's f*** buddy.

It is only after this that Julie gets drunk at the party (shown by her slow dancing with a waiter who's still holding a tray), starting to show how affected she was by her "status" in their relationship. It is safe to assume that she spent the rest of the party in David's house, or near it, and followed him to Sofia's house where she waited until the morning (she says that she missed an audition).

I believe that nobody told her, she always had the feeling that she is just a "friend with benefits" for him, and confirmed that feeling when catching him in Sofia's place.

This is explained in her wiki page:

She was his "fuck-buddy" and she knew it, though she would deny it to herself. When a young Latina woman, Sofia Serrano, entered their lives and Julianna knew David was in love with Sophia from the moment he set eyes on her. She would stalk him.

After David spent the night at Sofia's place, she followed him there, spent the entire night waiting for him to exit her apartment building. When David left the apartment the next morning, Julie chose to pull up and put a guilt-trip on him so he would get into her car.

Being a manipulative person, Julie throw it on Brian just to make the best friends fight.

"I never talked to her" he glanced sideways in a very telling way --Brian

So yeah he was indeed lying, this is further emphasised by the way they talked about her being a fuck buddy and how Brian was crushed by that.

He was drunk and bummed out that David was hooking up with his date so he probably blurted it out when Julie turned him down and even though that part is only alluded to , its pretty clear that he did.

The reason the movie doesn't show exactly what went on with Brian and Julie is because we are meant to suspect things from David's point of view, suspecting but helpless to realise the entire truth so weather he really did or didn't. And that is part of the experience of jealousy that the movie successfully conveys.