The Celtic boss is as disappointed as anyone they went out of the competition at the very first hurdle.
But Lennon reminded them they have so much still to play for - including resuming their Champions League campaign next week against Barcelona - so they should not waste time feeling sorry for themselves.
He admitted he had his say with the players in the dressing room immediately after the match, but insisted: "Analysing it now, we had 26 corners, and umpteen chances. We didn't get the rub of the green.
"We hit the post, and had one cleared off the line. But you always have to take your chances.
"I didn't think we created nearly enough in the first half. We were a little bit pedestrian.
"The new lads coming in maybe are not up to the tempo of the game yet.
"But I had to change it. I need to freshen the side up now and again because I can't keep relying on the same players.
"However, looking at that last night, I am going to have to go strong for a while until the rest get up to speed."
Lennon believes the enormity of what has happened will only hit some of his players when they reflect on it today.
He said: "Some of them probably don't realise yet, the new lads coming in, what it means.
"Certainly the senior boys will be sore.
"But it is no problem picking them up again. We will go to Kilmarnock strong-minded and determined to win the game.
"We have a big, big week coming up again.
"It's gone for me. I have dealt with it in the dressing room and I'm looking forward to the game on Saturday now.
"There is no conflict in the dressing room. I don't need to say too much. They already know. It's unacceptable, that result."
Lennon has previously tasted defeat in the final of this competition twice, and in the semi-final last year, but defeat to Allan Moore's side is the biggest punch in the solar plexus to his ambition to lift the trophy.
He said: "It's a sore one because I wanted to get to the final.
"It's the only trophy I've not won as a manager, but I will get over it pretty quickly. There is so much to play for this season.
"Will it be a blessing in disguise? I don't know because, if we go out of Europe by mid-December, there will only be two competitions to play for.
"It's very disappointing to lose at home, in particular.
"And, with the amount of chances, possession and dominance we had, not to score a goal was very frustrating.
"I can't say I saw it coming, but, you know if there is no tempo to the game it can happen.
"The number of times we put the ball across the face of the goal and we didn't get enough people in the box. We were crying out to get more players attacking the ball.
"To be fair to Morton, they defended heroically, and credit for that.
"But I have got to look at my own team's performance, And, apart from not putting the ball in the net, which is the most important thing in the game, it wasn't that bad.
"Were we unlucky not to score? Yes. Did we deserve to lose? No. That's football."