The social networking platform has been criticised in some quarters for failing to censor a controversial post by the President, but Zuckerberg has defended his approach in a meeting with Facebook employees.
Speaking in reference to the ongoing riots in the US, Trump recently warned: "When the looting starts, the shooting starts."
In response to the comments, Zuckerberg admitted he faced a "very tough" decision over how to treat the post.
He said, according to The Verge: "How to handle this post from the president has been very tough.
"It's been something that I've been struggling with basically all day, ever since I woke up ... This has been personally pretty wrenching for me."
Zuckerberg insisted he was unhappy with Trump's comments.
He explained: "My first reaction ... was just disgust.
"This is not how I think we want our leaders to show up during this time. This is a moment that calls for unity and calmness and empathy for people who are struggling."
By contrast, Twitter hid comments from Trump, saying the post violated its rules about glorifying violence.
The message was hidden behind a warning that read: "Twitter has determined that it may be in the public's interest for the Tweet to remain accessible."