What makes the loss of a flap track fairing strongly increase fuel consumption on Airbus planes? Inspired from this question about the loss of a flap track fairing.

In the answer by Thunderstrike, a part of the configuration deviation list of an Airbus A320 is linked. In it, it says:


  One fairing may be partly or completely missing. 
  
  Performance
  
  
  Fuel consumption is increased by 3.14%
  


That really is a lot!

I found a post on Airliners.net citing the CDL of a B757:


  Straight out of the MEL/CDL manual for the 757, The item falls under CDL 27-51-1 which states there are 6 installed [Flap Track Fairings, Remark] on the aircraft and up to one per side may be missing. No fuel burn penalty but there are a few small weight penalties, no speed penalty. Our A-300's with the same CDL item does have a 1% fuel burn penalty and only one can be missing out of the 10 installed. I see this item come up 3 or 4 times a year, no biggie.





What causes this very high increase in fuel consumption on Airbus planes?
What are the differences between the fairings of a Boeing and an Airbus (because Boeing has no increased fuel consumption, Airbus has)?
The fairings double as anti-shock bodies (or Küchemann carrots) and help to reduce shocks on the lower side of the wing. Below you see a wind tunnel test from the Vickers VC10 development where flow visualization using oil was used at Mach 0.9:



Wing without (left) and with (right) anti-shock bodies at Mach 0.9 (picture source). The light line on the left side indicates a strong shock which increases drag substantially over the situation pictured on the right where the flap track fairings have been used to smooth out the sudden reduction in cross sectional area from the rear-loaded wing airfoil.

Please read this answer if you are unsure why aircraft experience more drag as they approach the speed of sound. By stretching the aircraft body over a larger length, the gradients in the cross sectional area distribution can be made more shallow such that the air has more opportunity to make way for the aircraft.