It's normal and natural to feel bad - and I'd say that feeling is to be embraced. If you could kill a mouse in cold blood, through planning and with forethought, without feeling at all bad, then I'd worry for you.
You deliberately planned to kill an animal with a trap. An animal whose life and motivations you have some empathy for, some understanding of. Yes, you did this for your own peace of mind and well-being, but now you're comparing your actions and the outcome with the level of inconvenience the mouse brought.
Was it proportionate to kill the mouse because it kept you awake? I'm not looking for an answer there, just voicing the question that's inherent in the OP.
If you'd seen the mouse suddenly, and hit it with a broom, you'd probably feel less bad about it - there'd be adrenaline, there'd be a feeling of achievement perhaps. But instead, you set a fatal trap that the animal had no chance of escaping, that exploited the basic drives of the mouse - drives you are clearly empathising with - to kill it.
A mouse is a mammal, so we share a lot of brain structure - that's apparent in the way they behave, the decisions they make and so on. Unlike an insect or a spider, we can imagine the mouse's mind. Of course, they have no higher thought processes, but we can see ourselves in the mouse - so it's normal and natural to feel regret for its death.
Despite saying all this, which might seem like I'm saying "You ARE bad for killing the mouse", you shouldn't worry about your feeling. I'd recommend that you accept it, understand it, and in future act with the knowledge that you will feel bad if you cause harm to other living creatures.
In the short term, just know that there are "humane" traps, that catch but don't kill mice, so you can release them later. I checked, and the NZ Department of Conservation don't treat mice as an invasive species, unlike rats.
Full disclosure: I'm a vegetarian and an animal rights advocate. I'm also compassionate to our differences of opinion about animal welfare, and people's rights to their normal cultural practices - so I'm not here to say "Animal traps bad!" - I just want to say that "Forget about it" is a poor choice.