In order to escape from the eval block, you need to tell Perl something unexpected has occurred. This usually done with die, where you should check $? after each system command, a la:

eval {
    system("cp xyz.dat abc.dat");
    die "$?\n" if ($?);
    system("cp xyz.dat2 abc.dat2");
    die "$?\n" if ($?);
    };
if ($@) {
    print "Error occured: $@\n";
}
[download]

Please note the difference in reliable scoping between $? and $@ - as noted in Error Indicators.

Update: As JavaFan notes, this does not capture the actual error messages, only the error codes returned from system (as per your OP). If you want to handle the actual error messages, you'll need to capture STDERR, as per 781684.