In a match short on chances the Europeans benefited greatly from Chaouchi's handling, which had been suspect all game, with 11 minutes to go.
The 25-year-old misjudged former West Brom midfielder Robert Koren's shot from outside the area and when it bounced in front of him he bizarrely allowed the ball to go past, clipping his shoulder and hitting the net.
It was similar to the error England's Robert Green made in allowing the United States to equalise in their 1-1 draw in their Group C match last night.
"Everyone saw what happened with the ball, and what happened yesterday with England's goalkeeper," Saadane said.
"You have to adjust to the flight of the ball."
With the 'big two' in the group, England and the USA, drawing last night this game was an opportunity to seize a significant advantage and Saadane bemoaned his side's failure to do so as they now face England on Friday.
"We must recover and prepare for an even more difficult match against England, who are the best of the group," he added.
"It's going to be very difficult now. We had a great opportunity today and we missed it."
For Slovenia it was a totally different story as they leapt to the top of the group, registering their first points at the FIFA World Cup having returned home from their only previous appearance in Japan and South Korea eight years ago with three defeats.
The tournament's smallest country, with a population of two million, still have much to do to reach the knockout stage but this result has given them the necessary confidence boost.
"It was a mental victory," said coach Matjaz Kek.
"We wanted to win so much, so it's great for our confidence to get that win. Algeria had a mental advantage over us. They are used to big matches after playing in the African Nations Cup and had experience of important matches."
Kek sympathised with Chaouchi as he felt the specifics of the pitch at the Peter Mokaba Stadium - the grass has strands of artificial turf woven into it - played a part.
"I do not agree with this turf," he added.
"It's no excuse, it's the same for Algeria as well. But it is a different game on this surface."