This strikes me as a startlingly unusual way to do something standard. I take it you mean to use $exp as a matching expression and then use variable interpolation to get $1 into that string. See, here's the thing. You're working too hard and it's loads easier to make that work correctly. Your original string is interpolating $1 in before the regular expression is even executed. The critical change is to either use non-interpolating single quotes or to escape the $1 as \$1. Your first use of eval is completely superfluous and reduces overall legibility.

# 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\"";
  }
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Myself? Try this:

$exp = qr/\w+$/;
$str = "Logfile_Connection_Lost Hostname:";
$input = "DMSC0022 X10 oswald";

($hostname) = $input =~ m/$exp/g;
print "$str$hostname" if defined $hostname;
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That's more legible and will run faster as well.

Update: I completely rewrote the node since it sucked initially.