The singer was caught on camera as she spoke to Selena Gomez next to her, wiping a tear away and appearing upset.
Selena quickly linked arms with her best pal, and rested her head on her shoulder in an apparent act of support.
According to TMZ, Taylor was seen by cameras telling her: “I missed that note.”
Taylor Swift sheds a tear at the Grammys
Read more: Taylor Swift takes aim at Kanye West
The star opened the ceremony with Out Of The Woods – and despite wowing the audience, looked less than impressed.
Elsewhere in the show, Taylor responded to Kanye West’ s controversial lyric about her as she picked up the award for Best Album.
The singer, who is the first woman to win the award twice, shocked viewers as she referred to his song in her acceptance speech.
Kanye’s song Famous, which was unveiled last week, features the lyric “I feel like me and Taylor might still have sex. Why? I made that b**ch famous.”
In response to the comment, which has been labelled misogynistic, an emotional Taylor told the audience: “As the first women to win Album of the Year at the Grammys twice I want to say to all the young women out there: there are going to be people along the way who will try to undercut your success or take credit for your accomplishments or your fame.
“But if you just focus on the work and you don’t let those people side track you, someday when you get to where you’re going; you’ll look around and you’ll know that it was you and the people who love you that put you there and that will be the greatest feeling in the world. Thank you for this moment.”
Taylor was praised for her speech by many of the viewers, with one writing: “I am so proud of @taylorswift13 for that acceptance speech.”
But others thought she was letting Kanye win by speaking about him during her speech: “Taylor Swift wasted her album of the year speech to throw a shot a Kanye. Kanye wins again.”
Tori Kelly, who was watching the show, was caught looking very shocked as Taylor spoke – perhaps concerned how Kanye would respond this time.
Last week Kanye tried to deny that he was being disrespectful about Taylor with his song, tweeting: “I did not diss Taylor Swift and I’ve never dissed her… First thing is I’m an artist and as an artist I will express how I feel with no censorship.
“I asked my wife for her blessings and she was cool with it,” he said referring to Kim.
Tori did NOT look impressed
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He then claimed it was Swift herself who inspired the line.
Kanye continued: “I called Taylor and had a hour long convo with her about the line and she thought it was funny and gave her blessings.
“B**** is an endearing term in hip hop like the word N****.
“thing I’m not even gone take credit for the idea… it’s actually something Taylor came up with …She was having dinner with one of our friends who’s name I will keep out of this and she told him. I can’t be mad at Kanye because he made me famous! #FACT.” (sic)
While the rapper might have given his side of the story, according to reps for Swift, she advised him against the lyrics .
“She declined and cautioned him about releasing a song with such a strong misogynistic message,” her rep said.
“Taylor was never made aware of the actual lyric, ‘I made that b***h famous.”