How do I count zeros in sublists?

Try this example

matrix=RandomInteger[1,{5,5}] 

returns this

{{0,1,0,1,1},{0,1,0,0,1},{1,0,1,0,1},{1,1,1,0,0},{0,0,0,1,0}}

and then this

Map[Count[#,0]&,matrix]

returns

{2,3,2,2,4}

Another method (also reasonably general?)

0 /.(Counts/@myArray)