Steven Defour's withdrawal at half-time hampered Anderlecht claimed defenders Chancel Mbemba and Olivier Deschacht on Wednesday.
Defour - Anderlecht's "leader in midfield", according to Deschacht - was forced off with a thigh injury at the break in the UEFA Champions League clash in Brussels.
The home side had only hit the front just before half-time thanks to a diving header from Mbemba.
But with Defour replaced by Andy Kawaya in the second half, Anderlecht struggled and Galatasaray improved, although the Turkish visitors were eventually finished off by another Mbemba goal in the 86th minute.
"In the second half we lost Steven [Defour], who's our leader in midfield, and started dropping back," Deschacht said.
"We gave Galatasaray a few chances but luckily they didn't take them and we took control again."
Mbemba was thrilled with the "massive" three points, which clinched a UEFA Europa League berth for Anderlecht, who will finish third in Group D behind Borussia Dortmund and Arsenal.
"We did everything we could, we did not give up, and we got the three points. It is massive," the Congolese defender said.
"We have another crucial game on Sunday in order to defend top spot [in the league]. We will do everything we can.
"We managed the game well during the first half, then [Steven] Defour went off and we were under pressure a lot. Then the coach made changes and we held strong until the end."
Mbemba was also happy to have broken his goal drought this season, after scoring six goals last campaign, including five in the Belgian Pro League.
"I will not forget this game. I scored two goals," he said.
"I have not scored in the league [this season] but I have scored in the Champions League."