Let me explain this.
During recruitment processes with the exception of Graduate Trainee vacancies, employers usually prefer candidates who already have hands-on experience and can work with minimal supervision.
For instance, an employer looking for an Accountant will usually prefer to recruit one who can comfortably manage his finances with little or no supervision.
One who is proficient in various accounting tools because he has worked for years (even in a small company like ABC & Sons Limited).
They employer wouldn't want a Fresh graduate with no hands-on accounting experience (even with a 2.1 or 1st class). Fresh graduates usually require on the job training and training, as you know, comes with its own overhead.
My Advice:
Don't be to choosy. Everyone can't work at Zenith bank, Exxonmobil, Pwc or Nigerian Breweries at the same time. Working at ABC & Sons Ltd today doesnt mean you can't work at Chevron tomorrow. Be patient, it's not a race. Good luck Jonathan was once a Lecturer, today he is the President.
You could apply and take up smaller jobs from small companies where the competition is lower. Garner some experience and then apply to bigger companies. Later on, your years of experience will definitely give you an edge over other job seekers.
Trust me.