You'll want something like this:

#!/usr/bin/perl -w
$| = 1;

use strict;
use Fcntl qw(:flock);

my $count_file = 'counter.txt';

open( my $fh, '+<', $count_file ) or die( "open failed: $!" );
flock( $fh, LOCK_EX ) or die( "flock failed: $!" );

++ ( my $count = <$fh> );

seek( $fh, 0, 0 ) or die( "seek failed: $!" );
truncate( $fh, 0 ) or die( "truncate failed: $!" );

print $fh $count;

close( $fh ) or die( "close failed: $!" );
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