After Marco Reus and Sokratis Papastathopoulos scored for Dortmund, Hakan Balta's header briefly gave the Turkish outfit hope of a comeback.
But Ciro Immobile's breakaway strike and an unfortunate Semih Kaya own goal ended such thoughts.
Prandelli still felt his team put up a better display than when losing 4-0 to the same opponents in Istanbul.
"When you look at our performance, it wasn't a fair result," said the former Italy manager.
"The guys worked very hard and, compared to the first game in Istanbul, we have improved.
"We conceded the goals because of some small mistakes, but we'll get better in time."
Prandelli explained that striker Burak Yılmaz, who scored Galatasaray's goals in the 1-1 draw with Anderlecht and a 4-1 loss at Arsenal, was dropped to the bench for tactical reasons and due to a slight ankle injury.
The visitors must also now wait to see if UEFA impose any sanctions on them after the match twice had to be halted briefly due to away fans throwing flares onto the pitch.
