I'll preface by saying that I'm beginning to think I have the most abnormal hands in the world ... the basic Glock grip feels GREAT in my hands and my Ruger LCP, while not "fun" to shoot, is certainly not a chore or a pain. I don't trust it much beyond 7 yards. But I'm getting better the more I practice with it.
My first ever pistol was a Colt Mustang Plus II (basically a Colt Government .380 grip with a Mustang-length barrel and slide). It was a joy to shoot and I kick myself at least once a month for selling it to buy my Glock (though I do love my Glock, it is like any other Glock, the Colt .380s are becoming an expensive rarity). It shot better than Walther PPK by far. Have never fired the Sig 380 or Bersa, but like the feel of both guns (though the Sig is quite large for a .380).
Back to your question: The barrel on that Micro Eagle is even shorter than an LCP or Kel Tec, I think. And the LCP with grip extension has more space on which to squeeze your two middle fingers into some form of a "grip" on the weapon. The Eagle's construction and ergonomics remind me of the old AMT Hardballers. Solid, well-made gun. But feels like you're shooting the round directly out of the webbing between thumb and forefinger. My good-riddance Kahr PM40 felt like that when I shot it. My Charter Arms Undercover .38 felt like that.
I don't think it's the round. It's the gun. And I'm not saying this is a "bad thing" nor a "bad gun" just that it is so compact and the ergonomics are so tight, that it's never going to be fun (or accurate) to shoot. Many people also don't like the ergos on the LCP/Kel Tecs. I'm just lucky in that I don't think they're all that bad - though I'd rather shoot my Glock any day. Funny thing is, I took a colleague to shoot about a month ago. He's a bit of a noob and he disliked the Glock but LOVED the LCP. Actually shot the LCP BETTER than the Glock and better than even I could shoot the LCP and he'd never even touched it before and had only fired maybe three handguns in his life.
I think how a gun fits in your hand is the single most important facet of accuracy. All other aspects can be taught and learned. But if your hand doesn't like the gun, you'll never shoot it well. That being said, the greatest increases in accuracy I've found, especially from smaller carry guns (LCP & Smith J-frame) is regular dry firing - really concentrating on holding the gun steady in a solid, but comfortable grip, and working the trigger. The only difference between this and live fire is the recoil. Once I get my mind set that I've got a good grip and good trigger pull mechanics, the recoil can (but not always will) become an afterthought.
Lastly, not sure if there is a laser site available yet for the Eagle. But CT laser on my LCP has greatly increased my accuracy and confidence.