The January signing, who is a winner of the competition with Inter, is happy to have helped his new side reach the last eight, regardless of what happens later in the tournament
The Netherlands international believes the Turkish champions can be satisfied with their European campaign even if they bow out in the next round, which will be drawn on Friday, after knocking out Schalke in the last 16.
"We are in the last eight and that's already a big thing," the former Ajax and Inter star told Sky.
Galatasaray won the Uefa Cup in 2000 but have never tasted glory in Europe's premier competition despite regularly contesting the early rounds.
Sneijder lifted the trophy with the Nerazzurri in 2010 but played down his new team's chances of progressing beyond the quarter-finals.
"We'll have to wait for the draw but it will be difficult whoever we play, so I don't want to say that I would prefer 'this one or that one'."
"[All the teams Galatasaray might face] would be difficult, but it's already a pleasure to be in the last eight."
Sneijder credited Gala's passionate fanbase for carrying them through a seesaw tie with Schalke in the round of 16.
He added: "We have spectators all over the world and they always support us, they are amazing. The best fans in the world."