This doesn't exactly speak for your manager: Either he's not capable of concisely and effectively addressing problems with his reports (core management capability) - or he's trying to build pressure from nothing to keep you on your toes and working hard through fear.
Tread carefully around this guy so that you don't get hit by his incompetence or malice.
If you can, try to quantify his gut feeling and establish a paper trail:
- Ask him to come to you immediately when he sees something problematic with your work and let you know - so you can correct it asap, for everyone's benefit.
- Ask for regular meetings where you briefly clarify what you've done recently, what you're planning to do next, and what the current issues are. Take notes. If he never raises issues but complains later you can ask: Why was this never raised before? How can we ensure that problems get raised sooner, so that they don't cost the company a lot of money?
- Keep notes of issues resolved, features developed, etc. so that you can quantify your achievements.
Also, regularly but briefly report your / your team's achievements to him so that he associates you with good news (= good gut feeling). ("In the last month, we've implemented features X, Y, and Z and fixed the font size bug.")
I've seen "bad gut feeling" used by an overly busy boss who didn't have the time to regularly check in with all his subordinates and made their yearly evaluations up from the last impression / rumour he got about them. Of course, he couldn't quantify his gut feelings and then got angry when asked to explain. Unfortunately, the only thing that helped was getting the worker's council involved to make him back off and ultimately finding a better job...