The German escape artists have put on two faces in their games recently, including during their Champions League play-off against Sampdoria when they trailed 3-0 in the second leg before losing 3-2 to reach the group stage on away goals.
They managed to salvage a point in their opening Group A match against Spurs but luck may not be on their side throughout the campaign as they set their sights on a place in the last 16.
"This was a very weak game from us and I really hope this will be the exception in our group matches," said Bremen goalkeeper Tim Wiese.
"If we are to advance we really have to lift our game, be more consistent. We overslept in this first half," he said after goals by Hugo Almeida and Marko Marin cancelled out Tottenham's two early strikes on the English team's Champions League debut.
While Bremen had a disastrous first period, their battling performance in the second has boosted the side's confidence going into the next two matches against holders Inter Milan and Twente who also drew 2-2 in Enschede on Tuesday.
Bremen's top striker, Peruvian Claudio Pizarro, will soon be back after a muscle problem while Per Mertesacker and Naldo are also close to returning from injury to bolster the defence.
The two central defenders will be key to providing Bremen with consistency in the campaign as their backline looked in a sorry state of affairs for much of the game.
Spurs would have wrapped up the points with a third goal midway through the first half but for Wiese's goalkeeping.
"At least we are all top of the group," joked Bremen director Klaus Allofs. "But in all honesty it's a good result for us as we did not lose... We must really work harder from now on as there are no easy games in this group."
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