Do you want to advance at this company? When you leave it, do you want to be able to have great references from this group of people? If so, then, yes, you must socialize a bit more than you do. Any task on a job can be learnt, but what many employers want to see is the ability to get along with many different kinds of people and be an effective team player, if not leader. The only way to show that you can do that is by talking with and sometimes socializing with your colleagues.
They don’t have to be your best friends! But the occasional lunch with one or two of them, or speaking to them, asking for advice or help, making small talk at the water cooler for a few minutes in the morning; these things help.
I wasn’t very good at that at my last “permanent” job, and it’s hindering me now in my current search for work. Hardly anyone there knew me well enough that I feel comfortable asking them for help, reccos or references now. And I spent 8 years there. Don’t be like me. Don’t tell yourself that you won’t fit in or “Gee, it’s like high school in here!” That doesn’t help. Learn how to be social with your work mates. Unless you have the most top-notch skills in the world and headhunters are beating a path to your door in your field, you really need effective social skills. And even if they are, you still need effective social skills.
Try Toastmasters to learn how to be less afraid in speaking to others. Or a meetup group. Figure out where your shyness is coming from and work on lessening those issues. Your career depends upon you working on these things, it really does. Good luck.