Trabelsi's side played with an extra-man for the majority of the knockout clash after Woyo Coulibaly was dismissed with just 26 minutes on the clock for a dangerous challenge on Hannibal Mejbri.
But it took until late in the game for Tunisia to find the back of the net, as Firas Chaouat powered home a header on 88 minutes.
But a 96th minute penalty from Lassine Sinayoko took the tie to extra-time and ultimately penalties, where Mali emerged as 3-2 winners.
Speaking after the game, Trabelsi admitted Tunisia wasted a good opportunity to see off their opponents.
He said on Flash Score: "A defeat remains a defeat, even if it comes through penalties. It is true that we could have qualified, as our opponents played with ten men from the end of the first half, but it did not happen.
"The responsibility for the loss lies with the coach, that is certain. The players gave everything they had in a match we largely controlled, and we cannot blame them."
The coach added: "It was a difficult match. Tunisia were in control, but unfortunately after scoring, something incomprehensible happened and we made a mistake. Of course, there is great disappointment and pain after Tunisia's elimination from the competition."