I also learned regex from that book and had the same experience as you, so although I can't remember how that book worked it's magic (it's been nearly 20 years) I can corroborate your recommendation.
I also found the various perldoc pages on regex to be very helpful resource that I referred to frequently back when I was writing perl. Notable pages are perlretut [0], which serves as an intro to regex, perlre [1] which goes into considerable depth, and perlreref [2] which is a handy quick reference for day-to-day work.