The 19-year-old frontman suffered the injury while on loan with Conference side Braintree Town last week.
"That boy's career is more important. A tackle like that is horrendous. There is no room for it in football," he told BBC Essex.
Miller responded to Devonshire's comments on Twitter, insisting that he was fair and wishing Mensah a speedy recovery.
"Braintree manager needs to get a grip!" tweeted Miller. "My tackle was honest! Needs to look at his players first!
"Hope the Braintree lad is fine!! I never would intend to hurt anyone."
Mensah, whose contract with Watford runs until 2016, made his 10-minute first-team debut from the bench against Bolton Wanderers on November 23.