For the next one week, keep a log of all the activities that you do during every half an hour of your time and analyze. You may notice that you have been interrupted throughout the day by various events. In between interruptions you might have had some time to do what you wanted to do. Some interruptions you might have had some time to do related to your job. But most of the interruptions will be non work related. You will notice that you never had major chunk of time and your day was fragmented.
You have to do something to consolidate your time and concentrate on activities which you have to do. There is no point is saying that you did not have the time. The fact is that the available time went to do an activity which is not related to the task what you had accomplished.
One way to consolidate your time is to create unavailable time which you need to invest on activities which you have to do. An open door policy may be nice to hear. But if you do not know how to implement the same, you will get into problems since your time will be dissipated by various interruptions all through the day.