Bremen tomorrow [Saturday] take on Borussia Monchengladbach, another side who had high expectations at the start of the campaign but are finding the reality after seven games rather different.
After finishing fourth last season, Gladbach were keen to establish themselves as a force in the Bundesliga, like Bremen used to be until two years ago when they failed to qualify for Europe for the first time in eight years.
After overhauling their squad in the summer, Bremen targeted this season as the one which saw them return to Europe, but with just seven points to their name they are closer to the bottom three than the top six.
"Seven points from seven games are too few, it is time we moved up a gear," Allofs told the Kreiszeitung Syke newspaper.
"If we lose, then we know that we are down there. And we know what the atmosphere would be like around here.
"The coming weeks will show what the true potential of the team is."
Gladbach have enough of their own problems at the moment, with Switzerland international Granit Xhaka complaining of a lack of ambition and Mike Hanke of his lack of action.
Coach Lucien Favre gave assurances the two issues had been "dealt with internally".
"If we are compact and defend well, then we will get chances and we can beat any opponents," he said.
Only Alexander Ring is ruled out due to injury, but both Juan Arango and Patrick Herrmann should be fit to start.