anniyan,
Sometimes it is important to start out with functional code and then work on improving it to be "right". Have you considered making it two steps?

my @matches = grep { $_ !~ /(\&\&|\|\|)/ } split /(\&\&|\|\|)/, $str;
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This obviously isn't the way you want to leave the final code but it is better to having something that works that you are unhappy with then something that doesn't work at all. You can always improve. Commentary after the code snippet added