Such is life my friend. I think office jobs where you can actually call your work done at the end of the day are few and far between. You will probably either need to resign yourself to carryover work on a daily basis or you'll need to find another job. I don't think any employer will say you are being given too much work, particularly if they are not requiring you to stay late to get it finished each day. When I worked in an office, keeping a running to do check list was the best way for me to keep track of what needed to be done and what was already done. There was rarely a day when the checklist was empty by the end of the day.
Whenever you start out in a new job, your workload is usually lighter and you are given more responsibility as you master each task that is given to you. You can probably consider it a compliment that they feel you are ready to take on more work. Now, if they think you are not fast enough and that you should be getting more work done in a day, they will probably let you know that and you will have to find a way to speed your processes up if you want to keep your job. But more than likely, they expect that you will not finish everything every day and that as long as you are working efficiently and effectively, you are doing a good job.
You'll just need to put aside your "need" to get everything done every day. Surely you don't expect to get everything done at home every day, do you? Is your house spotless before you go to bed each night? Is every piece of clothing laundered and neatly hanging in a closet or folded in a dresser? Is every dish washed and in the cupboard? Is every trash bin empty and fresh and ready for tomorrow's trash? I'm guessing not. The same usually goes for work. :-)