To avoid some of the backslash confusion you can use the \xnn hexadecimal ordinal and a look-ahead.

$ perl -Mstrict -Mwarnings -E '
my $str = q{i am us$ing moni$ka expressi$on};
say $str;
$str =~ s{(?=\$)}{\x5c}g;
say $str;'
i am us$ing moni$ka expressi$on
i am us\$ing moni\$ka expressi\$on
$
[download]

I hope this is helpful.