The Leith outfit looked to be on course to rack up an emphatic victory after taking control inside half an hour courtesy of a Genseric Kusunga own goal and Ryan Porteous header.
However, Dundee somehow managed to recover by finding the net within three minutes either side of the break through Kenny Miller and Paul McGowan.
Lennon, whose team ended a three-game scoring drought but are now without a win in five straight games, admits a lack of quality on the ball and a mental fragility cost the hosts.
“It’s symptomatic of the spell we’re going through at the minute,” lamented Lennon.
“We don’t put teams away and we’ve conceded two poor goals by switching off.
“Some senior players are not playing at the level they could be and my strikers aren’t functioning at the minute either.
“It’s a culmination of things, it’s frustrating but it’s part of football and we need to get back to being strong mentally because that’s what we were good at for a long period of time and we’re lacking that at the minute.
“The positives are we’ve broken the run of not scoring goals and we’ve gained a place today.”
Hibs wasted little time in stamping their authority in the game after taking the lead just 40 seconds into the match.
Kusunga got a desperate header on Daryl Horgan’s cross with Flo Kamberi lurking behind him but the defender directed the ball into his own net.
Dundee ended a five-game losing sequence with a point in the basement scrap with St Mirren a fortnight ago but continued to look vulnerable during the opening exchanges in Leith.
Hibs were in the mood and should have doubled their lead in the 15th minute.
Horgan fed Martin Boyle inside the box but the newly capped Australia internationalist hit a shot across goal and wide instead of squaring a pass for the unmarked Kamberi.
Dundee’s forays into the opposition box were few and far between although Miller brought out a fine save from Adam Bogan in the 18th minute when the striker found space inside the box to get a header on Glen Kamara’s cross.
Desperate defending from the Dens Park club then denied Jamie Maclaren a goal as timely blocks by Kusunga and Cammy Kerr in quick succession spared Jack Hamilton’s blushes after the goalkeeper spilled a Lewis Stevenson cross.
However, Hibs did add to their tally on the half hour mark with a powerful back post header from Porteous from a menacing Stevie Mallan free-kick.
Dundee looked down and out as Hibs threatened to mete out a thrashing but the visitors reduced the deficit in first half injury time through Miller.
Nathan Ralph dug out a low cross from the left and Miller poked the ball past Bogdan from inside the six yard box.
Incredibly, Dundee completed the comeback less than two minutes into the second half as McGowan grabbed his first league goal of the season.
Jesse Curran took the ball off the feet of Mark Milligan before finding McGowan and the midfielder stepped back on to his left foot before curling an effort into the far corner of the net.
The Tayside outfit now looked like a completely different team to the one that found themselves down after 30 minutes and their cause was aided by the sound of the home fans turning on their side.
Both teams pushed for a winner but had to settle for a share of the spoils.
Dundee fell three points adrift of St Mirren at the bottom but manager Jim McIntyre hailed his side’s fighting qualities.
He said: “We got off to the worst possible start, it was a terrible start.
“After the second goal we disappeared a wee bit and looked fragile but we managed to get that all important goal that gave us a bit of belief back.
“At half-time we told them to be careful and that there’s opportunities here, be brave and pass it.
“I saw plenty of heart when we went behind to St Mirren recently but coming to Easter Road is a different kettle of fish, they have a quality squad and from that side of things we had to stand up to a lot.
“But equally I thought we were threatening ourselves and I’m delighted with the response.”