Fresh from holding Bayern Munich - last season's Bundesliga champions and Champions League runners-up - to a 0-0 draw over the weekend, Schaaf believes the level of performance his side showed at the Allianz Arena on Saturday stands them in good stead for the visit of Spurs.
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"Of course, we played very well in [Saturday's draw at Bayern Munich] but we have to improve some things," Schaaf told the UEFA website on Monday.
"For example, we did not score there and so there is room for improvement. After a year away, we start against a team from England and now we can compete with the best teams in Europe."
Bremen last graced the group stages of the Champions League two season's ago before bowing out to Greek giants Panathinaikos and last season's winner Inter Milan, who they also face in their group this year.
"We have a very difficult group with attractive teams. We want to create special nights in the Champions League like we did in past seasons. Of course we are missing [Claudio] Pizarro, Naldo and [Per] Mertesacker but we have a high-quality squad and we proved it in Munich."
As well as being optimistic about Werder's chances in this year's competition, Schaaf also had special praise for Spurs boss Harry Redknapp whilst singling out Tottenham's aerial threat as the biggest danger to his team.
"Redknapp is an excellent coach and he demonstrated it by getting his team through against Young Boys. Tottenham have a very good team and will be great opponents.
"I think we will see an interesting match. We have to pay special attention to Peter Crouch, because of his height. And he can always score. But [Bremen defenders Petri] Pasanen and [Sebastian] Proedl also have great qualities."
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