You'll want to preface each '\' in YOUR regex with (?<!\\)(?s:\\.)*). Try this code out:

while (<DATA>) {
  chomp;
  print "matched '$1' in '$_'\n" if /(?<!\\)(?s:\\.)*(\$\d+)/;
}
__DATA__
for the $1th time
SELECT * FROM Product WHERE Price LIKE '\$2.59'
using fore- and back-slashes for emphasis: \\$10/
escaping: \\\$6
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