Leverkusen boss Alonso admits side paid price for soft defending in Bremen draw
Werder twice came from a goal down to snatch a point and leave Leverkusen with a third draw in their last four league games.
"The fact that Werder could come back was down to both sides," Alonso said. "We were too soft in defending and they used their chances.
"We can and must defend better. At the moment we are missing a bit of stability. When we win it back then we will improve," said the Spanish coach, who led them to an unbeaten domestic league and Cup double last season.
"At the end of the day we cannot be satisfied having twice wasted a lead," Alonso said. "It is not the first time this has happened to us this season. There are things we need to correct."
Leverkusen's latest slip-up in the league has left them five points off leaders RB Leipzig in third place. They also drew 1-1 at Brest in the Champions League on Wednesday.
"This feels like crap," said central defender Jonathan Tah. "Like a defeat. We just have to keep defending until the last second.
"The goals we let in were frustrating. I feel responsible. But we will get the chance to silence those talking about us now."