Arsenal cruised to an easy victory at the Turk Telecom Arena on Tuesday, although the performance was ultimately meaningless as Borussia Dortmund made sure of top spot in Group D with a 1-1 draw with Anderlecht.
Ramsey stole the limelight in Istanbul in the 29th minute as he doubled his tally to make it 3-0 with a vicious half-volley into the top-right corner from 30 yards after Galatasaray had failed to fully clear a Joel Campbell corner.
And the Wales international feels the effort is one of the greatest goals of his career.
Ramsey told Sky Sports: "The ball came to me on the edge of the box and I had a go and thankfully it went in. It's up there with my best strikes."
Lukas Podolski was also on target twice in a hugely impressive display and, although Arsenal were left to settle for second in the group, Ramsey believes they can take plenty of positives from the triumph.
"We finished on a high in the group and now we're looking forward to seeing who we'll face in the next round," he added.
"We scored a few goals and took full advantage of the opportunities.
"We came here with a few players making their first appearance and it was nice to come here and nearly come away with what we needed to finish top."
Ramsey also revealed that a hamstring problem was the reason for his substitution at half-time, but stressed that the issue is not serious.
"I felt a bit of a tight hamstring at half-time," he said. "So I came off as a precaution with the game against Newcastle at the weekend."
