I actually already did toy with the idea of interpolating the output of grep into a string, but it turned out to fail to gain any ground; it works, but it's no shorter, plus to get identical output you would have to also set $" to '' (empty string), which takes additional keystrokes..

My 37 keystroke method:

sub invert {
    #234567890123456789012345678901234567
    join'',grep/[^\Q@_\E]/,map{chr}1..255
}
[download]

And now without join, but with double-quotish interpolation:

sub invert {
    #234567890123456789012345678901234567
    "@{[grep/[^\Q@_\E]/,map{chr}1..255]}"
}
[download]