You say you took the CCNA course, do you just mean you completed the academy modules at uni/college or did you actually go and do the exam and therefore have the CCNA qualification?
If you haven't sat and passed the exam, it doesn't help you a whole lot as anyone can do the course, even though there are tests involved, but many fail the actual exam.
What did you study? Was it a college course like an HND, or do you have an undergraduate degree? If you're a graduate and passed well, there's lots of graduate schemes with various large names you could look at, ranging from BT to Mi5 and BAE Systems.
If you're not so fixated on the hardware side of networking, then you'll do a lot of networking type work in many sysadmin roles at smaller companies. Larger companies tend to silo these departments off - e.g. DBA, Network Operations, Development Operations etc. A smaller company might not pay as much when it comes to total package, however there's the potential to be exposed to a whole lot more in a shorter amount of time.
If it is FE level such as HNC/D then you will be looking at more entry level roles as stephen said. Try if possible to aim for somewhere you know has the work you want to do in it, that will at least give you something to aim for and have you speaking with the people doing that work.
If you do claim to know the CCNA, be sure you actually do. Again this comes down to having the CCNA and just having studied for it. You would be expected to know subnetting to the point you can answer simple questions like, how many usable addresses does a /28 provide. You'll also want to know basic answers for the likes of VLANs and if you're going to a data centre, you'll want to know about the routing protocols including BGP which branches beyond the CCNA and is more towards CCNP. It just demonstrates your knowledge and interest.
Basically if you don't answer the simple questions, you're written off instantly if you claim to have a CCNA. Also if you haven't sat the exam, don't claim to have a CCNA because you're issued with a card, as in a credit card style. So if you were going to an interview you'd take it with you in your wallet as it has your number on it and expiry date, it is something you're expected to be able to prove.