You should use the .on
method:
$("#exampleGrid").on('focusout','.handsontableInput',function () {
alert("LLL");
});
JSFIDDLE: http://jsfiddle.net/edi9999/HEH5C/1/
The issue with your code was that at the moment of the execution of $(".handsontableInput")
, they was no element with this class, so the event was attached to no element.