Last season's German Cup winners, who have again qualified for the Champions League group stage after a fourth-place finish, had expected a faster start. Instead, they have now drawn their two league games after losing the German Super Cup to Bayern Munich last month.
"It has been a crap start, we can't say that enough," said Leipzig sports director Oliver Mintzlaff. ''Two points from two games is not what we had imagined.
"With all due respect to VfB Stuttgart and Cologne, these were tasks where we should be able to pick up six points, and we did not do that."
It had all looked better only a few weeks earlier, when Leipzig's all-time top scorer, Timo Werner (26), returned to the club after a two-year spell at Chelsea.
Domenico Tedesco's team also managed to hold onto Christopher Nkunku (24), the league's 2021/22 player of the season, despite a long list of major European clubs interested in signing him.
Werner scored on his comeback last week, as did Nkunku, but their team still had to settle for a 2-2 draw against Cologne.
Leipzig's next opponent, Union, will be arguably tougher than the previous two, with the Berlin club having finished fifth last season and already having double the amount of points as Leipzig.
Union have won their last three matches against Leipzig and are on a nine-game unbeaten run in the Bundesliga stretching back to last season - a club record.
"We are now already playing catch-up (in the Bundesliga) and have this tough task of going to Berlin," Mintzlaff said. "We have only won there once and it's uncomfortable for any team to play there. That is why it would have been important to have a good start."
Champions Bayern, leading the race with two wins from two matches, travel to promoted VfL Bochum on Sunday.
Borussia Dortmund, the only other team with the maximum number of points so far, can take a provisional lead if they beat Werder Bremen on Saturday.
