The explanation is as follows.
The atomic masses of the elements in a group increase from top to bottom.
Specific heat capacity is defined with reference to a standard mass of a substance, not on the basis of mole.
So, when we take the same mass (say 1 kg) of the elements in a group, the number atoms or moles decreases from top to bottom as the atomic mass increases.
This may be the reason for such decrease in the specific heat capacity of alkali metals from top to bottom.
Hope it answers your question.
All the best!