Though trailing 3-0 from the first leg, it seemed Bremen would give the Catalan side a torrid evening when they opened the scoring through Hugo Almeida after just four minutes, though their task was made almost impossible after Klose's sending off.
The Germany international was cautioned in the 3rd minute for leading with his elbow in an aerial challenge, then was shown his second yellow for diving to win a free-kick on the edge of the area.
"The referee's decision was unjustifiable," Schaaf fumed.
"The players were still fantastic, and they tried everything, but after 3-0 in the first leg and with a man down from the 20th minute it was all over."
Espanyol coach Ernesto Valverde admitted he feared the worst after's Bremen's opener.
"We didn't start well and that early goal was just what we wanted to avoid, but once we managed to score it was much easier," he said.
They will now face Sevilla in an all-Spanish final.