Some viewers said Davis was overly pursing her lips, with many complaining her facial expressions were distracting and insulting.
Speaking to BBC News, Davis said it is "incredibly hurtful when people say negative things about your work".
Criticism, she acknowledged, was an "occupational hazard" of acting.
"How do you move on from the hurt, from failure?" the 56-year-old asked. "But you have to. Not everything is going to be an awards-worthy performance."
Media outlets drew attention to the online criticism of her portrayal of the former First Lady - who is a lawyer and the wife of former US President Barack Obama - in Showtime's series.
The Daily Mail reported Davis was "mercilessly ridiculed" and drew attention to a plethora of critical tweets. One viewer called Davis's "exaggerated" portrayal "unnecessary and borderline insulting".
Another tweeted: "They set Viola Davis up by allowing her keep her mouth that way throughout the filming. It's so cringey and distracting."
Some viewers likened Davis's expression to "duckface" - a term which describes an exaggerated pouting expression, often employed by social media influencers. "Viola Davis's face must have been so tired," one user joked.
But in a trenchant riposte, Davis said: "Critics absolutely serve no purpose. And I'm not saying that to be nasty either.
"They always feel like they're telling you something that you don't know. Somehow that you're living a life that you're surrounded by people who lie to you and 'I'm going to be the person that leans in and tells you the truth'. So it gives them an opportunity to be cruel to you.
"But ultimately I feel like it is my job as a leader to make bold choices. Win or fail it is my duty to do that."
The star says playing someone as familiar as Michelle Obama was "almost impossible". "Either you're doing too much or not enough," she noted.
And she has no idea what the woman in question thought of her portrayal. "I don't have any personal contact with Michelle Obama," she said.
Davis is about to release her new written memoir, Finding Me. It is startlingly honest and, at times, a jaw-dropping read, charting her rise from poverty and abuse to becoming the first African-American to win the triple crown of an Oscar, Emmy and Tony for acting.
She won the Academy Award for best supporting actress for her role in a screen adaptation of August Wilson's Fences, which starred and was directed by Denzel Washington.
Davis won an Emmy for the TV thriller How To Get Away With Murder; and a Tony twice for King Hedley II, and Fences when it was on Broadway.
But she said she wrote the book partly because she doesn't want to "go to my grave" being known only for the above accolades.
"I have the awards on my mantelpiece but I have to tell you that when I'm going through anything in my life, that don't help me," she said.
"The awards, I'm extremely grateful for them. I am literally in shock I was able to achieve what I have achieved, knowing my beginnings. But that's where it begins and ends."
Caption: Viola Davis portrayed Michelle Obama in Showtime's TV series, The First Lady