First off, uncomment use strict;! Then add the my to declare each variable. Note though that you need to declare @Filenames outside the loop.

Note that #recursively search  $path for files is a lie. There is no recursion and the search will only find files in the top level directory. If you want to actually perform a recursive search you need to do a little more work. At that point File::Find is likely what you want. Taking that route, something like the following (untested) code is what you want:

#!/usr/local/bin/perl -W # force taint checks, and print warnings
use strict; # install all three strictures
use File::Copy;
use File::Find;

my $path = "sourceDirectory"; #define full path to source folder
my $newpath = "destinationDirectory"; #define  path to new folder
my @Filenames;

$|++; # force auto flush of output buffer
find (\&doCopy, $path); #Recursively search $path for files to copy

sub doCopy {
    return if ! -f $File::Find::name;
    
    chdir($path) || die "cannot move to $path";
    my $destFile = $newpath . $_;
    print "\$destFile = $destFile\n";
    copy( "$_" , "$destFile" ) or print "File $_ cannot be copied. $!\
+n";
}
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Note that you will probably have to clean up issues regarding paths to destination sub-directories in copy. You will probably need to do some magic with $File::Find::dir to strip off the root path and append the remaining path to $newpath.