Pre-tournament favourites Ivory Coast were 2-1 up on Sunday with one minute left after substitute Abdulkader Keita had found the back of the net with a superb 25-metre strike but the Elephants let the result slip from their hands.
Madjid Bougherra equalised one minute into stoppage time before substitute Hameur Bouazza earned World Cup-bound Algeria a place in the last four when he headed home in the opening minute of extra time.
"When we were 2-1 up with one minute remaining, we should have locked everything down and just sat back to keep that result," coach Vahid Halilhodzic told reporters.
"This is unacceptable. A great team would have regrouped in the bow and, no matter what, would have won the match."
Halilhodzic, who was undefeated in his last 23 games with Ivory Coast, added his players failed to sustain the pressure of being favourites.
"I had told them during training on Thursday, 'be careful, do not take Algeria lightly, they have nothing to lose'," he said.
"I feel like the pressure of being the overwhelming favourites was simply too much for some players."
Ivory Coast will not have that problem when the World Cup finals kick off in South Africa in June as they were drawn with Portugal, Brazil and North Korea.
But Halilhodzic was also concerned his team were struggling during key moments.
"Every time, Ivory Coast slip at the wrong time," he said, referring to the 2008 African Nations Cup semi-finals, when Ivory Coast were thrashed 4-1 by eventual champions Egypt.
"This team comes to a sticking point when they need to show their talent."
Chelsea striker Didier Drogba was far from his best throughout the match against Algeria, missing a couple of clear-cut chances that would have sent his side through.
The defence, led by Manchester City centre back Kolo Toure, proved shaky on Algeria's long crosses and on set pieces.
"On every corner kick, they would win the ball," said Halilhodzic.
"We knew they would send long crosses and yet, numbers 13 (Karim Matmour) and nine (Abdelkader Ghezzal) won a lot of balls and caused huge problems to our defence."
