The international chart-topper had been heavily tipped to walking home with both Best Original Song and Best Actress.
A Star Is Born was also nominated for Best Film – Drama, as well as Bradley Cooper picking up nods for Best Director and Best Actor.
However, despite the film topping box offices around the world the flick only won the Best Original Song category for Shallow.
Gaga, whose real name is Stefani Joanne Angelina Germanotta, lost out to the title of Best Actress to Glenn Close.
Meanwhile, Queen and Freddie Mercury flick Bohemian Rhapsody closed off the night by winning Best Film – Drama.
Elsewhere Bodyguard’s Richard Madden was the best actor in a TV drama and Olivia Colman scooped the gong for best actress in a comedy or musical for her role as Queen Anne in The Favourite.
There were also successes for Christian Bale for his role as Dick Cheney in Vice, and Ben Whishaaw after he starred as Norman Scott in A Very English Scandal.
But as the evening wrapped up, Twitter was quickly awash with angry fans of Gaga.
“WOW. A Star Is Born got robbed. I’m so mad. How did Gaga and Bradley not receive anything besides best song,” one viewer raged.
Another added: “Lady Gaga was robbed.”
“Bradley Cooper and Lady Gaga were robbed,” a third continued.
A fourth moaned “Lady Gaga deserved Best Actress and Bradley deserved Best Director hands down as well as Best Actor.”
Reigniting the seemingly never-ending feud between Lady Gaga and Madonna, one fan tweeted: “Lady Gaga lost to Glenn Close but Glenn Close lost to Madonna.”
Both Madonna and Lady Gaga now have two Golden Globes to their name.
Madonna won Best Actress in 1997 for her portrayal of Eva Perón in Evita.
Then in 2012 Madge took the gong for Best Original Song for Masterpiece from her 2011 film W.E.
Meanwhile, Gaga first won a Golden Globe Award in 2016 beating out the competition to win Best Performance By An Actress In A Limited Series Or Motion Picture Made For Television for her role in American Horror Story: Hotel.
Bodyguard star Richard Madden said of his success: “You constantly question yourself as an actor, if you’re good enough, if you’re real enough or if you’re deserving of anything and that’s a constant thing that you’re doing for yourself.
“Kind of questioning your ability, so to even be nominated was a real confidence boost in terms of thinking ‘I am doing this, I can do this’.
“And then I’ve won it. So I’m kind of blown away by it because I’ve been active for 20 years, never thinking you’re good enough, I suppose. And then to receive something like this, I suppose it’s a wake-up call to me to be like, believe in yourself more because other people do.”
Golden Globes 2019 Winners List
Best Motion Picture – Drama
Bohemian Rhapsody *WINNER*
If Beale Street Could Talk
A Star Is Born
Best Motion Picture – Musical or Comedy
Crazy Rich Asians
Green Book *WINNER*
Mary Poppins Returns
Best Performance by an Actress in a Motion Picture – Drama
Glenn Close (The Wife) *WINNER*
Lady Gaga (A Star Is Born)
Nicole Kidman (Destroyer)
Melissa McCarthy (Can You Ever Forgive Me?)
Rosamund Pike (A Private War)
Best Performance by an Actor in a Motion Picture – Drama
Bradley Cooper (A Star Is Born)
Willem Dafoe (At Eternity’s Gate)
Lucas Hedges (Boy Erased)
Rami Malek (Bohemian Rhapsody) *WINNER*
John David Washington (BlackKklansman)
Best Performance by an Actress in a Motion Picture – Musical or Comedy
Emily Blunt (Mary Poppins Returns)
Olivia Colman (The Favourite) *WINNER*
Elsie Fisher (Eighth Grade)
Charlize Theron (Tully)
Constance Wu (Crazy Rich Asians)
Bradley Cooper (A Star Is Born)
Alfonso Cuaron (Roma) *WINNER*
Peter Farrelly (Green Book)
Spike Lee (BlackKklansman)
Adam McKay (“Vice”)
Best Performance by an Actor in a Motion Picture – Musical or Comedy
Christian Bale (Vice) *WINNER*
Lin-Manuel Miranda (Mary Poppins Returns)
Vigo Mortensen (Green Book)
Robert Redford (The Old Man and the Gun)
John C. Reilly (Stan and Ollie)
Best Supporting Actress in a Motion Picture
Amy Adams (Vice)
Claire Foy (First Man)
Regina King (If Beale Street Could Talk) *WINNER*
Emma Stone (The Favourite)
Rachel Weisz (The Favourite)
Best Supporting Actor in a Motion Picture
Mahershala Ali (Green Book) *WINNER*
Timothee Chalamet (Beautiful Boy)
Adam Driver (BlackKklansman)
Richard E. Grant (Can You Ever Forgive Me?)
Sam Rockwell (Vice)
Best Original Score in a Motion Picture
Marco Beltrami (A Quiet Place)
Alexandre Desplat (Isle of Dogs)
Ludwig Göransson (Black Panther)
Justin Hurwitz (First Man) *WINNER*
Marc Shaiman (Mary Poppins Returns)
Best Original Song in a Motion Picture
All the Stars (Black Panther)
Girl in the Movies (Dumplin’)
Requiem for a Private War” (A Private War)
Revelation (Boy Erased)
Shallow (A Star Is Born) *WINNER*
Best Screenplay in a Motion Picture
Barry Jenkins (If Beale Street Could Talk)
Adam McKay (Vice)
Alfonso Cuaron (Roma)
Deborah Davis and Tony McNamara (The Favourite)
Peter Farrelly, Nick Vallelonga, Brian Currie (Green Book) *WINNER*