The former Chelsea striker and fellow Ivorian Emmanuel Eboue were subjected to monkey chants from the crowd as Fenerbache won the match 2-1.
Drogba, whose Galatasaray team have already secured the Turkish championship, wasted little time in highlighting that both Fenerbahce goals were scored by Cameroon striker Pierre Webo.
|Unimpressed: Galatasaray's Didier Drogba has hits out at racist abuse he received|
Drogba said on Galatasaray's Facebook page: 'You call me monkey but you cried when Chelsea beat Fenerbahce in 2008, you called me monkey but you jumped in front of your screen when I won the Champions League.
|Unimpressed: Drogba responded to Fenerbahce fans' abuse|
|Chill out: Drogba tries to calm the situation down|
|Abuse: A supporter of Turkish football club Fenerbahce holds a banana in his hand as Galatasaray players arrived|
'I didn't wave the banana with the aim of racism, I just joined a jeering against (Galatasaray goalkeeper Fernando) Muslera.
'I am not like that. I apologise to Fenerbahce and Galatasaray fans,' he added.
|Smoke and fire: Fenerbahce fans light flares during the bad-tempered derby|