Ozil, 24, departed the La Liga powerhouse for London, with Arsene Wenger's men forking out more than £42 million for the German midfielder.
And Ramos, who is preparing for Spain's World Cup qualifier against Finland in Helsinki, was shocked by Ozil's departure in the shadows of the transfer window's closure.
"He was a very close team-mate and friend," Ramos said of Ozil.
"Like all his team-mates would tell you, I had a very good relationship with him and had a good feeling about him.
"He's a great guy and it's a real shame to let a great player like that go, and from my own perspective it's sad to see a friend leave the team. I wish him the best but obviously it's a shame."
"As one of the captains I welcome him to the club. We are very happy to have signed a player like Bale because he is a great player and can do a lot for us," Ramos said of Real's £85.3m acquisition.
Ramos' club and national team-mates Isco and Alvaro Arbeloa were similarly disappointed at Ozil's departure, although the former was not as surprised given Bale's impending arrival.
"I knew Bale was coming because the press was there every day asking the same questions," Isco said.
"We all know he is a great player and I'm sure he'll help us a lot."
"He kind of gave a farewell speech on Sunday but I thought he was joking," Arbeloa said.
"I didn't pay much attention to it yesterday, but for all the fans it will be a big loss because Mesut was the sort of player who made you believe, not just for the way he played, but also because of the type of person he is.
"He got on well with everyone: fans and us players. It's normal to see it as a big loss."
