Dougie Imrie fired Saints ahead early on at Dens Park, but Dundee dominated the second half and goals from John Baird and Jim McAlister secured a rare three points for the home side.
Lennon said: "It was Jekyll-and-Hyde stuff from us. It means getting into the top six now is going to be a very tall order.
"We got off to a dream start but never took it on and I didn't expect what happened to happen.
"The way we took our foot off the pedal is the most disappointing thing about this defeat.
"I decided to try to freshen things up beforehand by making a few changes so maybe I've got to look at that aspect as well.
"We spoke before the game about how fired up Dundee would be as John Brown is a real motivator.
"But we let them back into the game when we shouldn't have which is our own fault."