The Patriots problem hasn't been low round drafting, which is where it's more difficult to find hits. The problem has been high round drafting, where finding hits is easier. The problem, draft-wise, has been missing picks at the top, decisions regarding retention of picks (one can argue the right or wrong of keeping players, but the discussion here is about the picks) along with blown picks when they were available. Here's the top two rounds of picks, post-2011:
2012: Didn't keep Chandler Jones, Hightower's been oft injured, drafted Tavon Wilson
2013: Didn't keep Jamie Collins, drafted Aaron Dobson
2014: Drafted Dominique Easley, drafted a QB and then didn't keep him
2015: Drafted Malcom Brown, drafted Jordan Richards
2016: Drafted Cyrus Jones
2017: Drafted Casper the ghost, maybe, because they didn't draft any live humans
2018: Drafted Isiah Wynn, drafted Sony Michel, drafted Duke Dawson
High/low is irrelevant when the top end of your draft over the past 7 seasons is giving only what it's yielding in 2018. Plenty of obvious choices were passed over in the making of the above picks.*
*I get the injury issues with the 2018 draft, but we can only go by what we have at the moment.