Senegal let their early lead slip four minutes from time in the last 16 clash when they gave away a penalty, allowing the Ivorians to equalise for 1-1 and force the game to extra time and penalties, where the hosts won 5-4.
"It was a bizarre match," said Cisse of an encounter where the Video Assistant Referee (VAR) missed a studs-up tackle from Senegal's Sadio Mane that should have resulted in him being sent off before half-time.
However, the referee from Gabon then did not award the Senegalese a second-half penalty when Ismailia Sarr was tripped. It would have offered them a golden chance to double their lead and make it harder for the hosts to come back into the contest.
Ivory Coast then won a penalty late in the game after a lengthy consultation with VAR.
"There were a lot of strange incidents in the game but there is no need to go into that," said Cisse, who has been Senegal coach since 2015 and took them to a first-ever Cup of Nations title two years ago and qualified them for two World Cups.
"My only regret is that after the goal, perhaps we lost the main thread of the match a little. We jumped the lines too often even though we started this match well by controlling possession.
"I'm disappointed with the result obviously, disappointed especially for my players and disappointed for our people who expected a lot from us. But I'm also proud of my boys. When you lose, you have to maintain your dignity."
Senegal were the only side to win all of their group games and looked set for another victory when they went ahead in the fourth minute through Habib Diallo.
"We led until minutes from time. I think we got a penalty but the referee didn't go to see the VAR. They had a collision in the penalty area and then he went to see the screen. Today the decisions were against us, but so be it," Cisse added.
"When you look at our first matches, and when you also see the performance we gave here, truly, I think we deserved to go to the quarter-final. But that’s how football is."
