What you are doing is not exactly procrastination.

Postponing the task due to inability to do it is all right. Doing trash stuff instead of it, on the contrary, would be procrastination.

Imagine your brain to be a muscle. If you overstretch without resting, it will tire itself out. Obviously, you cannot conserve energy during the day by not using it, because it will "leak" anyway. You need to "flex" it - interleave periods of work with periods of rest, until it becomes comfortable for you.

There are good points that you can get, for example, from http://www.huffingtonpost.com/leslie-davenport/chronic-fatigue_b_1013186.html :

• if you wake with energy in the morning and find yourself dragging in the afternoon, the fatigue may have a physical origin
  
  [...] Eat a good breakfast, pick up the apple instead of the candy bar, get to bed at a decent hour and when you're stressed remember, "This too shall pass." And research is showing we're chronically dehydrated, which is an energy zapper. Eight glasses of water per day can do wonders. Because exercise builds vitality, try taking the stairs instead of the elevator at work, or a short walk as part of a lunch break (commit to a walking buddy if you tend to procrastinate.) And if you haven't had a physical in a while, it's worth checking for other common fatigue culprits of modern life, such as a vitamin D deficiency.

• if you wake up tired in the morning but get going as the day progresses, it's worth exploring your emotional concerns
  
  [...] So what burdens are you are carrying mentally that keep you from being present in the moment to your family, to your friends, to yourself? The shift is as simple as remembering that you have a choice where you place your attention. It's always an option to take a deep breath and look at the trees instead of the worries inside your head.

• While certain kinds of fatigue need targeted remedies, such as a medication adjustment, all types of depletion can benefit from rest and relaxation.

Also, try to clearly separate your work (day) from your home (evening). If you continue to drag a burden of the whole day, it will ruin your free time. An activity may help: going to the pool, taking a bicycle ride, basically whatever will grab your attention for a short time span, thus freeing you from the previous thoughts.

If you find yourself postponing tasks because you have too much in your head already, take out a pen and paper and write those things down for tomorrow's daytime, to get them out of your head.