Your question is yet another example where using strict and warnings makes things a whole lot easier to understand:

print ("a", "b")[1];
print qw(a, b)[1];

__END__

# Result:
syntax error at x.pl line 3, near ")["
Execution of x.pl aborted due to compilation errors.
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But when you add those 2 magic lines at the top:

use strict;
use warnings;

print ("a", "b")[1];
print qw(a, b)[1];

__END__

print (...) interpreted as function at x.pl line 5.
Possible attempt to separate words with commas at x.pl line 6.
syntax error at prog.pl line 5, near ")["
Execution of x.pl aborted due to compilation errors.
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That line about "print (...) interpreted as function ..." is what others (eg. mreece and jdporter) have already discussed.

Another way of looking at it is that:

print ("a", "b")[1];
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is the same, precedence-wise, as:

(print ("a", "b"))[1];
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which doesn't make sense (ie. is a syntax error).  You have to force the desired precedence with:

print (("a", "b")[1]);
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The line "Possible attempt to separate words with commas" is just alerting you to the fact that instead of:

print qw(a, b)[1];
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you probably actually meant something more like:

print qw(a b)[1];
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