Most Uni (including the 'top' ones) are fine about combos of BTEC and A levels so you don't need to write 'excuses' for doing a BTEC.
BTECs have more practical application within the course than most A levels and this is a major advantage that you need to stress in your PS. Pick out some project work that you did, use this to show your enthusiasm for the subject and demonstrate that you understand that a degree is about much more than just learning 'theory'.
How you do all this does depend on your BTEC subject and your intended Uni subject area, but having a BTEC is not a disadvantage that you need to apologise for!