So in my current, 5th attempt or so (pirate spam early game sucks. Also Shakturi) I noticed that even though I have a total research capacty of 3700k and an empire potentional of 1303k my research output is only around 1350k.
Whats up with that? Why am I losing 2000k in output?

Capacity is how many labs of that type you have.
Potential is how many of those labs can be run by your current population.

In the specific case you mentioned, you have built more labs than you can run which is why the numbers don't line up.
You're not losing any output - you just don't have the population needed to achieve that level yet.
To get more research you need more population.

Ideally, your lab capacity shouldn't exceed your research potential by much.
It's not the end of the world if it does, all it means is you're paying maintenance on something that's not giving you anything in return.