Having claimed just eight points from their opening six matches of the season, Barcelona currently occupy 12th place in the LaLiga standings and were unable to improve on their position after playing out a 1-1 draw against a 10-man Deportivo Alaves on Sunday.
The result saw the Catalan giants equal the record for the club's worst-ever start to a season in the three-point era, matching the return of fellow Dutchman Louis van Gaal's maligned 2002/03 squad, who ultimately ended the campaign in sixth place.
With two wins and two draws from their opening six matches, Koeman has also registered the worst start by a new Barcelona manager since Rinus Michels, another countryman of his, claimed just one win and two draws over the same period in the 1971/72 season.
"It happened to us against Juventus and today as well. Furthermore, we gifted Alaves their goal. But if we create that many chances, we can't miss so many. If you create chances and you only score one, it's not good.
"Of course, I'm worried that we've only picked up two points from the last 12 [available]. I think the play has been, in general, very satisfactory. I'd be more worried if we weren't creating chances."