The Dee were 2-1 up and had a man advantage over the hosts after Steven Caulker scored on his debut, but they imploded in the final 20 minutes.
First Kris Boyd scored and then Iain Wilson came off the bench to poke home a brilliant solo effort – his first for the club – to seal a dramatic 3-2 win for in-form Killie, who now have seven wins on the trot at Rugby Park.
It left McCann seething with his players after they had worked hard to put themselves in pole position.
“I just cannot fathom what goes through players’ heads at times when you’re trying to manage games,” he said.
“The (equalising) goal itself is appalling.
“There was no professionalism in terms of getting into space and that created the space that Kris Boyd lives in. It was a super finish but he shouldn’t have had that.”
On Wilson’s winner, he added: “I thought it was a foul on (Glen) Kamara and it wasn’t given.
“He waltzed right through the middle of the pitch so it’s quite appalling to lose a game when you go up like that.”
Referee Nick Walsh came under particular scrutiny from both sides throughout the match after sending off Gary Dicker and awarding the visitors a penalty for a handball by the same man.
He also sent off Dundee assistant Graham Gartland after the winner, but McCann refused to blame the officials.
He said: “The only problem I had was I thought it was a foul in the lead up to the third goal. I thought it was the right decision for the red card but couldn’t quite see the penalty and I don’t know if it was deliberate.
“It wasn’t the referee that cost us the three points, it was themselves.”
For Killie, it was a result that moves them to the brink of the top six and marks a seventh successive win at home for the first time since 1979.
And despite being reduced to 10 men, Steve Clarke was always confident they would take something from the game.
“We were never dead and buried,” he said. “It’s always difficult with 10 men but with this group its never dead and buried.
“We have great character, good quality and we showed it tonight.”
On Wilson’s winner, Clarke added: “He’s been injured but when I came in everybody told me he was a good player and a good prospect, and I think you got a glimpse of that tonight.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.