They threw away a one-goal lead at Schalke to lose 2-1 to the Royal Blues and miss the opportunity of breaking into the top five, and Schaaf admitted such games were becoming a recurring nightmare.
"We have seen games like this all too often this season," he said. "We play well, but don't get anything tangible.
"Once again, we have not rewarded ourselves for our efforts. That's our biggest fault and we don't like it one bit.
"I can live with the performance, but not with the result. We're not going to give up, though."
Bremen's director of sport Klaus Allofs, who refused to rule out a move to Bundesliga rivals Wolfsburg, was equally frustrated with the result which ended a three-game unbeaten streak.
"This defeat is annoying because it is unnecessary," he said on his club's website.
"We were too wasteful and, in games like this, there is no mercy for so many mistakes.
"Now we have to start all over again, starting against Dusseldorf next weekend."
Whether Allofs will be there next weekend is unclear. He is reported to be wanted by Wolfsburg and he neither denied nor confirmed an interest.
"Things can change quickly in football," he told Sky television.
"The fact is I have a contract until 2015, but you know that is no guarantee that I stay so long.
"Of course I have heard that they are interested, but I have not had any contact, nor held any negotiations with them.
"To speculate about it does not get us anywhere, though."