Goals from Pierre-Emerick Aubameyang (2), Marco Reus and Adrian Ramos ensured that BVB maintained their 100 per cent record in Champions League Group D, a far cry from their league form, where they currently sit just one point above the relegation zone.
"It is a little different in the Champions League. We have a little more space for our counterattacks," Hummels explained to Sky.
"Our aim was to strengthen our defence and not to commit easy mistakes. We were shocking in that respect against Koln [in the 2-1 defeat on Saturday]. Tonight we were very effective.
"We scored beautiful goals and that made it easier. For us it was important to stay on course in the Champions League. And now we have to get back on track in the Bundesliga after five really bad matches in the league."
Galatasaray boss Cesare Prandelli conceded that his side were no match for Dortmund and the Istanbul-based outfit are now bottom of the group with just one point.
"We played against a really tough team," he said to Smartspor.
"Borussia Dortmund are a complete side and have been very successful in the Champions League in recent years.
"We must improve but our primary target is the Turkish League. The Galatasaray board brought me here for the league title, for the fourth star. Now we must focus on the championship."