Real's midfield and defence were overrun time and again by energetic Werder, shorn of their most influential player, Diego, on the night.
Schuster admitted: "We gave them too much space when defending. All three goals were down to poor marking. We gave them too much time.
"When we had the ball, everything was fine, but once it was lost we did not work hard enough.
"I won't blame just the defence, everyone was generally poor."
Schuster also said: "You could see the attitude of Werder. They have foreigners, but they possess the winning mentality of German teams. It's difficult to face such teams."
Ruud van Nistelrooy missed an open goal at 2-1 and the coach said: "In the second-half, it could have been 2-2 and within seconds it was 3-1. The game was there for the taking, but Ruud missed."
Asked about Robinho's substitution, Schuster added: "He was worn out. He was already tired in Murcia. It was due to fatigue from the last games and also being away with his national team."