The holders have won just once since lifting the trophy back in March and their miserable run continued as they slumped to a 2-1 second-round defeat against Queen of the South.
The match at Palmerston went to extra-time after a goalless 90 minutes but the Buddies looked set to progress after Steven Thompson's header put them in front five minutes into the additional period.
But Stephen McKenna struck a stunning leveller for the Scottish Championship side before Michael Paton clinched victory five minutes from the end of extra-time with his clever lob over David Cornell.
The upset was Saints' third defeat from four matches this season and Lennon admits he has no idea why his team are playing so badly.
He said: "Plain and simple - we have let ourselves down, we have let the club down and more so the supporters.
"We had enough chances to win the game but the fact is we didn't take them.
"We know how much it meant to us last year to win this competition and words can't describe how much it hurts to go out at the first hurdle.
"It baffles me that we have only won one game since the cup final, especially with the quality we have. I know the character that the boys have and winning games breeds confidence. But that's something we're just not doing."
Queens boss Jim McIntyre said: "It was two special goals to win it and it is a fabulous result.
"To come from behind shows tremendous character but I know the boys were capable of this after they picked up a few big cup wins last year. It's great to get another one so early this season."