Why is it said that for efficient transmission of radiation, antenna size should be comparable to wavelength of the radiation?
An electromagnetic field is produced by an accelerating charge.

For a given fixed charge and acceleration, you can increase the radiated field by accelerating that charge over a longer distance.
  A longer wire might also allow you to accelerate more electrons for a given fixed current into the wire (before the current reflects back off the end).

So radiation resistance is roughly proportional to (d / lambda)^2 .  For a given current, this is proportional to amount radiated away from the system as EM energy (rather than heat or mechanical energy.)

An antenna much shorter than a half wavelength just doesn't have a lot of distance over which a given charge can accelerate during a half cycle of an oscillating drive source.  So is less efficient.

But once the acceleration distance approaches a full wavelength (or longer), due to the speed of light and propagation time of the accelerating charge, parts of an antenna can end up radiating EM waves of the opposite phase from other parts of the antenna.  These opposite-phase waves can then interfere and cancel each other out at certain angles (such as broadside in the far field).  Which is inefficient in those directions.