Well first of all, don't feel too disheartened as you still have a 2.1 overall. Most master's courses ask simply for a 2.1; some will ask for a 'high 2.1' which often means around 67+ (this is the case for some Cambridge MPhils for example), while some very competitive master's courses will ask for a first. But if the requirements are simply a 2.1 then you have a chance.
As regards how to improve your essays, here are a few thoughts:
* you mention a few times that your use/lack of sources was criticized; often lecturers will expect you to go beyond even the recommended reading for an essay, and to find relevant literature yourself if you want a very high grade. This doesn't have to be daunting: see what sources are being cited by your recommended/required reading, and then go find that material to look at; use search engines such as your library's search tool or even Google Scholar to find extra sources.
* a second big problem can be lumped together under 'structure': you said your essays were disjointed, and certain themes weren't addressed, etc. A lot of these problems could be solved by paying close attention to how you organise your essays. Make sure you have a very clear introduction, where you lay out the big arguments/themes of the paper, and also a strong conclusion. Spend some time before sitting down to write by writing out a structure; maybe initially you can brainstorm some ideas, using the notes you've taken, then think about how you can fit the major points together so that they move from one to the other in a logical way. Don't jump from A to C and then back to B: really think about how all the points fit together, and how you can make smooth transitions between them. For my essays I had a numbered plan beside me while I wrote, with each paragraph laid out with bullet points of what I was going to argue, the evidence/sources I was going to use, and so on.
* Finally, before you even begin any of this, it's worth spending some time really examining what the question is asking you to do. It's too easy to simply read the title quickly, spot certain key words and assume the essay is about Topic X, when actually a very careful reading of the question will reveal that yes, it is about Topic X, but it also requires you to address Topics Y & Z in order to prove your point with regard to Topic X; I hope that makes sense! Really understanding the question will also help you when it comes to structure & making sure all the key themes are covered, as well as directing your reading and research properly.
I hope this is of some help!
EDIT: One final point - make sure you are actually advancing an argument in your essays!! An essay that simply regurgitates information will never score well; for an essay to do well, it needs to have an argument. This will involve weighing up the arguments in the sources that you read, and then making a case for whichever you find most convincing, while also acknowledging the positives in those arguments that you don't necessarily agree with as much. In essence, your essay must have a POINT to it - again, this links back to reading your question carefully, as this will often direct you with regards to potential arguments. A question may take the form, for example, of a statement, followed by 'Discuss' or 'Do you agree?'. Take a position! Don't simply recite both sides and then conclude by neatly summarising the arguments; take a position & argue it, using the sources that you have read while researching.