Mrs Clinton was filmed as she walked through the US Capitol while locking arms with husband and former President Bill Clinton.
The ex-Secretary of State appeared to be in a sombre mood as she walked through the building following her shock defeat on November 8.
At one point, Mrs Clinton is seen taking a deep breath and letting out a deep sigh.
Hillary Clinton arriving at Donald Trump's inauguration
I’m here today to honor our democracy & its enduring values. I will never stop believing in our country & its future
Some Twitter users have since tweeted in response to her appearance at the inauguration event.
“Such humility & sacrifice for the country. Thank you Pres Clinton & Sec Clinton. We treated you poorly. History will repair our breach,” said @riotwomennn, while @ahopeweiner added: “That is real strength.”
Another user, @llr517, said: “The strength women have when we're constantly screwed over for mediocre, dangerous men. What a world to live in.”
Donald Trump becomes 45th U.S. PRESIDENT
Fri, January 20, 2017
The inauguration of Donald Trump as the 45th President of the United States will mark the commencement of the four-year term of Donald Trump as President and Mike Pence as Vice President. A public ceremony will be held on Friday, January 20, 2017, on the West Front of the United States Capitol Building in Washington, D.C.
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U.S. President Donald Trump gives a thumbs up after being sworn in as the 45th president of the United States on the West front of the U.S. Capitol in Washington
Donald Trump was sworn in as the 45th President of the United States
However, at the event, some Donald Trump supporters chanted “lock her up” when Mrs Clinton was announced on the inauguration stage.
According to Twitter users at the event, she was booed along with her husband.
“Crowd boos and chants ‘LOCK HER UP’ when Hillary and bill clintons names are called,” said @melanie_metzman, and @TeddyDavisCNN confirmed: “@hillaryclinton: gets introduced -boos throughout crowd, a ’lock her up’ audible & separate ‘that's not nice’ from disapproving T supporter.”
Mrs Clinton also tweeted in the lead-up to Mr Trump being sworn in.
She wrote: “I’m here today to honor our democracy & its enduring values. I will never stop believing in our country & its future.”