Even if the task was not properly explained, you have the responsibility to ask key questions before, during and upon completion of the task if need be. Putting the blame on your supervisor will not cast you in a very good light. Another tactic is to blame someone else. Perhaps the task required a number of people to complete. Surely one of these people should have caught the mistake before completion.
Managers are concerned with mistakes.
Even more so, however, they are concerned with ensuring that mistakes are not repeated. By admitting your fault you're saying that you are willing to take responsibility and you're willing to work on methods to make sure the mistake is never duplicated. Again, this is not a bad idea. Letting your supervisor know that you feel terrible about making the mistake in the first place will most likely help them see that you realize the significance of your error and that you will be more careful in the future. You might be close, but let's be real here.