Constants in Perl declared with use constant are actually subs. The regex in m/.../ first goes through double quoted string-ish interpolation, and the general way to interpolate a sub call within a string is:

$var = "foo @{[ sub() ]} baz";  
# Note: This calls the sub in list context, so may have a 
# different effect than if called in scalar context.  Use 
# ${ \sub() } for scalar context.
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Also, the /e modifier is for the s/// operator, not the m// operator, hence the syntax errors you are getting.

So you would want something like:

print "attribute 0=\t$1\n" if m/@{[ATTRIBUTE_0]}='(.*)'/;
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It looks kind of ugly, but it works.