Verheijen, who briefly took charge as caretaker manager following the death of Gary Speed in 2011, has repeatedly aired his outspoken views about the United boss.
Following United's League Cup semi-final defeat to Sunderland on Wednesday night, Verheijen once again criticised Moyes on Twitter.
He said: "Over the last 6 months, Moyes' prehistoric training methods, poor player management & superficial tactical knowledge have been exposed.
"Obviously, first of all, David Moyes is responsible for creating total chaos with exactly the same players who won the title last season. Sir Alex Ferguson is responsible for appointing a relative nobody as his successor allowing him to stay in charge behind the scenes.
"But if you do appoint a nobody, at least make sure the coaching staff stays rather than the nobody appointing his clueless coaching friends."
United are currently seventh in the Premier League.