SQL & PL/SQL :: Can Insert A Table In Case Of Exceptions

Is it possible to insert a table in case of exceptions. For example, i have a function like this:

Create or replace Function test_function(p_Parameter_ID number) Return number is

l_Variable number;
Begin
Select output into l_Variable from test_table where id=p_Parameter_ID;
Exception when others then
Insert into exception_Table values('No Data Found', p_Parameter_ID);
return l_Variable;
End test_function;

In this function, if you notice, i wanted to populate an exception table for further analysis in case data is not found. The function gets compiled without any error in this case.However when i execute this and the Select query does not return any output for a particular parameter_ID, then the exception part fails. It gives me an error "cannot perform a DML operation inside a query".

Can't i write insert statements inside the exception section?