She added that "just 10" of this year's 600-strong cadet intake to Sandhurst were from black, Asian and minority ethnic (BAME) backgrounds.
Responding to Ms Griffith, Defence Secretary Penny Mordaunt said: "Of course defence can always do more."
The Armed Forces, she added, were "one of the greatest agents for social mobility in this country, one of the largest education providers in this country", adding "we ought to continue to encourage them to do more".
Watch: How officer cadets at Sandhurst train for conflict situations.
Speaking during Commons defence questions, Ms Griffith said: "At a time when Army numbers are consistently falling, it's all the more important that we draw on the widest possible pool of recruits."
She continued: "I know the Secretary of State is personally committed to creating a level playing field, so could she set out what she will do to seek out the brightest and best from all backgrounds."
Ms Mordaunt replied: "The numbers are actually not decreasing in terms of our trained and untrained strength and the recruits coming in.
"Those numbers are actually going up, but social mobility is incredibly important.
"Of course defence can always do more, but I think that across our Armed Forces they are one of the greatest agents for social mobility in this country, one of the largest education providers in this country and we ought to continue to encourage them to do more."
Ms Griffith said: "I'm a little bit disappointed at that answer because I think when we're talking about officers, there is a lot more that can be done and it's not just those from state schools who face barriers.
"Just 10 out of this year's 600-strong cadet intake to Sandhurst are from BAME backgrounds, just 10, and according to the MOD's own statistics, the regulars and reserves are also missing the Government's 2020 targets for BAME representation.
"So will the Secretary of State now commit to a root and branch review of recruitment barriers so as to ensure that we have properly staffed and fully representative Armed Forces."
Ms Mordaunt replied: "We already have a very clear idea about what barriers exist and what barriers existed in the past, that is why our community engagement programmes are so important and why since coming into the department I have protected those budgets."