9:01 AM PT -- Tallulah Willis is coming to mom Demi Moore's defense amid speculation the actress snubbed Kylie Jenner at the Golden Globes.

Demi's daughter with ex Bruce Willis posted to her Instagram Stories Monday, where she defended that there wasn't a "snub of any sort" following Demi's big win on Sunday. She explained the Willis family had recently spent the New Year with actress Elle Fanning, which is why DM hugged her instead of KJ.

She added ... "Had she seen KJ wanting to congratulate her she would have fully given her the time and space. Literally just give it all a break and let a gal enjoy her accomplishment."

Kylie Jenner didn't seem to have "The Substance" to warrant a hug from Demi Moore after the actress shocked audiences with a big Golden Globes win Sunday night.

Check it out ... moments after the 62-year-old star won her first-ever major acting accolade of her career, she took in an abundance of praise from fellow A-listers in the crowd ... including Elle Fanning and Kris Jenner's youngest.

However, Demi only seemed receptive to love from Elle, who she scooped up in a big hug ... blatantly ignoring the lip kit mogul's own congratulatory message.

Kylie appeared to take note of the snub, too ... she eyed Elle up and down before turning her back to the chatting actresses after she appeared to be iced out.

Watch the video ... Demi lovingly grabbed the "A Complete Unknown" actor by the hand while Kylie's beau showered her with praise.

Of course, it didn't take long for fans to catch wind of the snub ... with several fans coming to KJ's defense and calling out Demi for some alleged "cattiness."

To add insult to injury, Demi went on to accept congratulations from Kylie's boyfriend, Timothée Chalamet, seconds later.

Others defended Demi, however ... noting the reality star is "nobody" to Demi, so she didn't have to make time for the businesswoman after HER big moment.

Though, the awkward encounter didn't seem to dampen Kylie and Timothée's night ... the often-private love birds were seen locking lips later in the ceremony.

You may recall Kylie recreated Demi's iconic "Striptease" movie poster pose -- fully in the buff -- for Halloween last year, and Demi later reposted the image to her Instagram story, commenting “Love this!!”

We've reached out to Demi's and Kylie's reps for comment ... so far, no word back.