The Germany international secured a deadline-day switch to Arsene Wenger's side in a €50 million deal.
Ramos concedes he will miss Ozil on a personal level and believes the 24-year-old is a "unique" player.
"It's obvious that he is a special team-mate and friend," Ramos told reporters. "I've always had a real friendship with him, and it's a shame. He's a great footballer, unique.
"Everyone is free to choose the best for themselves, but if I were to decide what was happening at Madrid he would be one of the last who would be going.
"But he has decided, and the club too. We have a great team and I hope it will be a big year [for us].