Barca had lost just one of its previous eight fixtures in all competitions heading into Sunday's (AEDT) clash with Cadiz, which had already claimed the scalp of champion Real Madrid this season.
The only defeat in that run came at the hands of Atletico Madrid in Barca's last away outing in LaLiga, however, and its poor form on the road under Koeman continued as Alvaro Gimenez and veteran forward Alvaro Negredo clinched another famous win for Cadiz, which had just 17.9 per cent possession.
Cadiz moved up to fifth, while Barca sits 12 points behind leader Atleti, which overcame Real Valladolid 2-0, with its tally of 14 points from 10 league matches its lowest since 1987-1988 when adjusted to three points for a win.
Barca had 21 attempts, but only eight hit the target, and Koeman's side had to rely on an own goal from Pedro Alcala to get on the scoresheet at all.
The Blaugrana have failed to win four straight away LaLiga games (D1 L3) for the first time in a single season since 2007-08 under Frank Rijkaard.
The result was one that Koeman planted firmly on his players, insisting that their attitude on their travels has not been up to scratch.
"We can't concede a second goal like that. It's a lack of concentration," Koeman said of Negredo's goal, which came when he charged down Marc-Andre ter Stegen after Clement Lenglet failed to control a throw-in.
😱 "What was that??" Just when you thought it couldn't get any worse for @FCBarcelona, this! Defeat at @Cadiz_CFID, and embarrassment, too, after a mix-up that would have had a schoolboy side blushing! See all the highlights here 📺 https://t.co/1F47iv8Sqm | #LaLiga | #CadizBarca pic.twitter.com/yJzVxeZPQa— beIN SPORTS (@beINSPORTS_AUS) December 5, 2020
"It's hard to explain what happened because we had a good week. I think the first half wasn't good. We lost a lot of balls. There was a little improvement in the second half.
"It's a giant step backwards to be able to compete for LaLiga. I'm very disappointed. There are many points dropped away. If we do not improve the attitude away from home, there is nothing else to say.
"We have ups and downs in our games, in our attitude, although in principle it is good, but there are moments that it is not.
"When we don't have the ball, we fail a lot. This is an attitude [problem] of the whole team."
Barca has conceded first in its past four away league matches, a trend which concerns Koeman, who claimed his team is letting in the types of goals his former clubs have not.
"In away games they put us behind and that's more complicated," he continued.
"We don't have spaces to play and also, and we have to know this, we conceded goals that I couldn't think of happening in other teams that I have coached.
"It is very difficult to explain, it may be because we lack concentration, we lacked aggressiveness, but it is not easy to explain how we conceded the second goal."
Next up for Koeman is a home clash with Juventus in the UEFA Champions League, although the pressure is somewhat relieved as both sides have already qualified for the Round of 16.