Traveling solo is oddly freeing. You're by yourself, in a country in which you know nobody. You can reinvent yourself, and be whoever you want to be. There are downfalls, that being since no one knows who you are, you don't have anyone to turn to if something goes wrong.
Luckily, that doesn't happen often. If you're smart about things and are constantly aware of your surroundings, traveling alone can be far less terrifying than it seems.
There are ways to make solo traveling less lonely, like staying in more social hostels, or using Couchsurfing. By using these methods, you're never truly by yourself, because you're almost constantly surrounded by other people who are either your hosts, or who are in the exact same boat as you. Often hostels will host pub crawls, free walking tours, and social events that get people out of their rooms and socializing. Some of the best friends I've made while traveling have been met on pub crawls or hostel social events. As well, finding a hostel with an open kitchen and living space will put you in an environment where you're more likely to talk to people. Find a delicious smelling meal to cook so you lure new friends into the kitchen!
Couchsurfing is also an excellent way to meet people from the city that you live in, and can give you tips and tricks of how to get by in the local culture (it's also free!) Often times, they'll cook you dinner or take you around to show you the city if you're lucky!
Another excellent way to meet new people is by doing group facilitated tours instead of wandering around by yourself. I'm a huge proponent of wandering freely with no destination, however, group trips are a great way to see parts of the country you wouldn't otherwise see, as well as meet new people. You'll often find many other solo travelers on these trips. There are many options for day trips wherever you go, as well as week or month long tours such as Contiki that offer more social options for solo travelers.
There are definitely ways to assure that you're never truly by yourself while budget traveling. Being alone is a great way to meet new people, and there are always tons of other people in the same boat as you, so don't be afraid to strike up a conversation and say hello!