Another tweak should improve performance again:

#! perl -slw
use strict;

my @words = do{ local @ARGV = 'words.txt'; <> };
chomp @words;

my $all = join ' ', @words;

my $start = time;

for my $i ( @words ) {

    while( $all =~ m[ ([^ ]*$i[^ ]*) ]g ) {

        my $j = $1;
        next
            if $j eq $i
            or $j eq "${i}s"
            or $j eq "${i}'s";
        print "$j contains $i";
        last;                     ## Added
    }
}

printf STDERR "Took %d seconds for %d words\n",
    time() - $start, scalar @words;
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