Is it possible to get a slow leak straight after installing new tires? So I decided to replace my bike tires to Gatorskins to prevent punctures.

Anyway, so I installed them and they seemed to be okay. I had checked it a day or two afterwards and it was okay. But this morning, after 3 days, I see the tyre is flat again.

I hadn't rode it since putting the new tires in (well I rode it quickly round the block to see how it went but that was like 2 minutes). So I'm struggling to figure out what happened. I know sometimes installing a new tire, you can accidentally puncture the new tube and that's happened a few times for me. But they're usually because I've left the sharp object in the tire or I've damaged the tube somehow when trying to install it. Usually if I stuff it up like this, the leak will be apparent and I'll know straight away.

But this time I'm putting in new tyres and I also used a new inner tube. And the leak took several days so hole must be very slow. Since I haven't rode it, it must've been from me installing it, but what could've caused this? Is it possible to get a slow leak from installing a new tire?

Could it have something to do with the tubes I've used? Maybe they're defective?
I would more suspect a leaking valve. 
If you pinch the tube putting it in then it is typically not a slow leak.

If the valve is removable the pull it and look for any debris or defect on the seat. 
I had a set of cheap tubes that had like 1/2 loose valves. 
Remove it with pressure in the tire to blow out debris you cannot get to.