perlre can:

\Z Match only at end of string, or before newline at the end
\z Match only at end of string

Update Consider:

my $str = "The quick abc";

for my $regex ('\babc\z', '\babc\Z') {
    print "Matched with newline using $regex\n" if "$str\n" =~ $regex;
    print "Matched without newline using $regex\n" if $str =~ $regex;
}
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Prints:

Matched without newline using \babc\z
Matched with newline using \babc\Z
Matched without newline using \babc\Z
[download]