Whilst others are correct in pointing out that the best perl solution for the task at hand involves basename, those suggestions don't point out what your problem here is - which will bite you in the arse whenever you try to use $' and similar on the command line. That is, you need to understand the black art of shell quoting. This:

perl -we '$x="/foo/bar/ncak.030610.141654";$x=~/.+\// && print $'\'
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works, at least with the bash installed on this 'ere OS X box. What it does is single-quote all your perl up to and including the last $. It then ends the single-quoting, and immediately - with no intervening space - provides a single-quote. The single-quote is escaped so that the shell doesn't try to start a new quoted string and complain when it can't find the closing delimiter.