Modric signed off with victory over Real Sociedad, leaving after over 12 years as a Madridista.
Former Barcelona and Sevilla star Rakitic, now with Hajduk Split, said of his former Croatia teammate: "It made me very sad, because we all want to continue enjoying ourselves with Luka, but Luka at Madrid.
"Imagining a Madrid without him is quite difficult. Real Madrid has had great players, like Cristiano Ronaldo and Sergio Ramos, but Luka was different. He had everyone's affection.
"In March, when he was here in Split with the national team, I spoke to him and I saw that he was enjoying life. Modric needs Real Madrid and vice versa. Seeing Luka like this is not easy."
It surprised me
Rakitic also said on El Partidazo: "It's all very nice, the tribute... it's the first time we've all seen the 'boss' in the stands with tears in his eyes. It saddens me a bit.
"The only thing I've told him on the phone these days is that I hope he continues to enjoy himself and that he can take our national team (Croatia) to the World Cup.
"It really surprised me. But for me, as a friend, the most important thing is that he's happy."