According to Business Insider, the Meta CEO said Musk didn't spend long enough deliberating on the staff cutbacks he implemented.
Both tech firms have recently laid off thousands of employees, informing them via email.
However, Musk's firings were sent out to their personal ID and blocked all access to Twitter's systems.
Zuckerberg, who just fired 11,000 people, takes "full" accountability.
He said in a video: “I know there must be a range of different emotions. I want to say, upfront, that I take full responsibility for this decision. I am the founder and CEO and I am responsible for the health of our company, for our direction, and for deciding how we execute that including things like this. And, this ultimately my call, and it was one of the hardest calls that I had to make in the 18 years of running the company."
Musk - who bought Twitter for $44 billion last month - is being sued by multiple Twitter employees for allegedly conducting a mass layoff in violation of the Worker Adjustment and Retraining Notification Act, which requires employers to give at least 60 days’ notice ahead of being sacked.
He is also struggling to hold on to the site’s existing revenue streams after several advertisers quit over fears that the platform will no longer be a “safe place” for brands.
Famous faces including Whoopi Goldberg have also exited the platform, with the comic, 66, saying it had got “messy” since Elon’s takeover, while horror writer Stephen King, 75, blasted the billionaire should pay him for staying on Twitter instead of charging for a blue tick.