Second-half goals from John Baird and Jim McAlister cancelled out Dougie Imrie's early opener, with the result leaving the Paisley boss seething – and admitting a top-six finish was almost out of reach.
He 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 (interim manager) is a real motivator.
"But we let them back into the game when we should not have, which is our own fault."
Lennon took a gamble and made five changes from the team that pushed Celtic close in Saturday's William Hill Scottish Cup quarter- final for this trip to the only side still below the Paisley men in the SPL.
To be fair to him, his men sat 17 points above a Dundee side who had only amassed 15 in total during the season so far.
However, after watching his troops fail to cash in on a string of decent chances, thanks to an outstanding display by Dee veteran No.1 Rab Douglas, Lennon must now worry about a negative mindset before his side's Scottish Communities League Cup final later this month.
The visitors took control early on with the impressive Paul McGowan twice going close Sam Parkin's header was also cleared off the line by Gary Irvine.
Gradually Dundee, with Brown prowling his technical area restlessly, fought back and both Irvine and Gary Harkins went close with stinging 20-yard drives at Craig Samson's goal, but both failed to hit the target.
However, with 20 minutes gone home hopes took a severe knock when Lewis Guy slipped Imrie through the middle of the Dee back line and he dispatched high past the helpless Douglas from eight yards.
But with Saints failing to cash in on their string of chances Dundee hit back.
With 13 minutes gone of the second period Baird surged through the heart of the visiting rearguard and bent a superb 20-yard effort round Samson.
With home hopes rekindled Dundee surged forward and after some mesmeric dribbling by Harkins his back-post cross was knocked down by Brian Easton for McAlister to poke home.
Despite the introduction of Lennon's big guns from the bench in the form of Paul Dummett, Steven Thompson and Esmael Goncalves, it was not enough to stop Dundee claiming their first SPL victory of the year and their maiden win under Brown.
With the Buddies now seven points adrift of their sought after top-six status, with just 12 available to them before the split, this backfiring gamble to leave out some of his star men has had a clear and immediate impact.
Yet with Brown's resurgent Dundee now reducing the deficit between them and Saints to 14 points, it could be that the greatest implication of this disappointing defeat will come much later if a Dens version of the Great Escape is completed.
