One workaround is to use a negative look-ahead plus a dot instead of a negated character class: 

use strict;
use warnings;
use 5.010;

for (qw/'abc' "abc" 'abc"/) {
    if (/(?<FQ>['"])(?<content>(?:(?!\k<FQ>).)+)\k<FQ>/s) {
        say $+{content};
    }
    else {
        say "Not matched: $_";
    }
}
__END__
abc
abc
Not matched: 'abc"

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In reply to Re: Named capture backreferences cannot be used in character classes? by moritz
in thread Named capture backreferences cannot be used in character classes? by BrowserUk

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