I'm sorry you are hurting.
It seems to me as though there's a few things not quite right in what he says.
People who drink together are not true friends. They are friendly only because they like the shared hedonism, not because they genuinely know and like each other. As soon as the hedonism ends, so does the "friendship."
Drinking loosens inhibitions; some people use it to help overcome their shyness with others. But it often results in bad choices and actions, and much forgetfulness about what was said and what happened - hence no genuine connection.
How does your guy define "cool"? Does he mean fashionable? Into all the latest crazes? Popular? Hot? Not over-emotional, not disturbed by anything?
What do the two of you talk about when together?
Do you have different or similar interests?
Who are his friends? If they are not drinkers, what do they prefer doing? Why can't he spend time with them in other contexts?
Loneliness is not about whether we are actually alone. It is relative and different for everyone.
We can feel lonely if we don't have enough people in our lives, or enough depth and quality in the relationships we have.
From what he's told you, it doesn't sound like you are the problem; it sounds like something coming from inside him.
Extroverts need to spend time with others to feel energised; feel drained by two much time alone. The more extroverted they are the more people they need. The most extreme is like a butterfly or bee, insatiably visiting every flower.
The extreme introvert feels drained by too much time with others and needs lots of time alone to recharge. Most introverts prefer 1 -4 really good friends, like these relationships to be deep and intimate, and two or three hours together is enough.
Each of us is somewhere on the scale between introvert and extrovert.
Maybe your boyfriend is more extroverted than you are. If that's the case, then his need is no reflection on you. He would be that way no matter who his girlfriend was.
I feel uncertain saying the following...
If you want the relationship to succeed long term, try encouraging him to have time out drinking with his mates and meeting and socialising with others.
The tests will be:
Does he actually meet and develop new friendships this way?
How drunk does he get? How does he treat you when he gets home? How much and how often does he drink in general?
Is he at risk of becoming a drunk by trying to medicate his loneliness?
What is lacking in his social skills that means he needs to drink in order to socialise? (Coffee is far more effective.)
If he lacks conversation and communication skills, would he be open to developing them?
Would he be open to developing friendships in other ways - eg, joining a wood or metal work class, playing sport, volunteering, joining a hiking group, etc?
The last and hardest issue is something you might already fear.
Is he perhaps losing interest and planning to hunt for a new girlfriend. Many young men care more about sex than relationship; when they have a girlfriend it's not for who she is but for a regular means of relief. If this is the case, they tire of a girlfriend quickly and soon want something new. I say something because they are using like a doll, not loving her as a person. If this is the kind of bloke your man is, then letting go would be your best option. When you've finished grieving and grokking the lessons, you'll find it easier to attract and meet someone more mature and more suited to who you are.