# Use a regex object so it's compiled only once
$exp = qr|^DMSC0022\s+\S+\s+(\w+)$|;

# Use a non-interpolating string (or escape the $1 as \$1
$str = 'Logfile_Connection_Lost Hostname: $1';

# I can only assume you are assigning to $_
# because this is a snippet from some larger code. On it's
# own this is really weird. Normal code would do something
# like "DMS ..." =~ $exp instead.

$_ = "DMSC0022 X10 oswald";

# Force $exp to execute (don't just eval it, this is more correct)
if ( $_ =~ $exp )
  {
    # the eval() is still needed to force the source code
    # to generate. This is still silly.
    eval "print \"$str\"";
  }