Hassen's goalkeeping blunder proved the tipping point but not before the former French youth global saved Senegal's 80th minute spot-kick to force the game into extra time.
It will be a second final for Cisse, who was captain when Senegal made their only previous appearance in 2002 to lose on penalties.
"I want to congratulate Senegal and him for what they have achieved".
Senegal dominated the first half, producing seven shots to Tunisia's two, with Mane spurning their best opportunity when he missed an open goal.
"I have experience in playing high level matches and major competitions including the AFCON and this will allow me to manage the pressure of the match".
"This is football and we understand the whole team disappointment".
Senegal Lions of Teranga face off against the Carthage Eagles of Tunisia in the first semi-finals with the former targeting only their second final in history.
"I am the number one supporter of Aliou Cisse".
The manager continued "We hope this year will be the right one".
The advancement of both Algeria and Senegal to the final created a renewed sense of entitlement on social media from Kenyan fans, most boasting Harambee Stars "finished third" since they were in the same group with the finalists.
Niang swivelled inside the box before firing well wide and Mane rounded the goalkeeper but his shot from an acute angle finished off target. Tunisia had the first after 72 minutes which Ferjani Sassi missed while Senegal had their own in the 80th minute, missed by Henri Saivet.
Giresse took off Msakni at half-time and introduced Naim Sliti, scorer of the stoppage-time goal that sealed a convincing last-eight win over giantkillers Madagascar.
Sassi took the penalty himself but it was weak and Senegal goalkeeper Alfred Gomis saved easily.
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