Gaga didn't bring Christian with her to the ceremony - despite him being in attendance at other events this season such as the Golden Globes and the Screen Actors Guild Awards - and also didn't thank him during her acceptance speech when her song Shallow won the best pop duo or group performance prize.
The report comes after it was previously claimed the A Star Is Born actress was "over the moon" about her engagement.
A source said in December: "Gaga is so over the moon at the moment. She is constantly telling those close to her how grateful she is to be at this point in her life and work with such incredible artists and be with the man she loves so dearly.
"Gaga is incredibly elated about her engagement."
The source also then claimed Christian was "so proud of her success".
They added: "Christian loves to make her happy and he is so proud of her success. He is patient because he was a huge influence in her doing the film to begin with. The amazing thing about their relationship is that he understands her work and career and he is there to guide her.
"This relationship is different because Christian understands her on a more intimate level. She trusts him fully and feels totally secure around him. They don't get a lot of private time, but when they do, they love to have private getaways in fancy hotels."
- Bang! Showbiz
