The smaller eyes may work ok. Baits without a "flat" for eye placement I find will have one edge lifting up off the bait and that's the first point for problems in my opinion. I have mixed feelings on eyes. I think they look great and are outstanding as sales features, but in the panfish world they may or may not be needed, depending a lot on the mood of the fish. My jigs generally will not have eyes on them but I do carry a couple in each color and size with eyes in the off chance that the pannies are negative and studying the bait before hitting....then eyes can help. A little. I feel the color, bait isxe/profile and action play a larger part. Keep in mind my thoughts are centered on crappies and panfish here. I'm working with the smallest of the baits and eyes can be a tough challenge.
Bass and pike sized plastics afford a little more leeway. You could try heating a table knife just a little and pressing down on the end of your carrot to create a slight flat for eyes. It would take a little time but maybe worth it and wouldn't do a whole lot to hurt the rest of the plastic. The one thing I have found true with playing with these plastics is that there is a world of tricks a guy can use to easily manipulate the stuff. As for eyes, I definitely like larger eyes if at all possible. I use 3 and 4 mm eyes on different sized plastics, but really like BIG eyes on a smaller bait. It makes or gives the illusion of fear to the bait and I think customers see that and respond to it too.