The 29-year-old joined Los Blancos in 2009 from AC Milan, but a series of injuries left the Brazilian struggling to recapture the form which saw him named FIFA World Player of the Year in 2007.
However, Kaka has been handed an extended run in Jose Mourinho's starting lineup this season and deputy Karanka claims that Madrid are reaping the rewards.
"He has had a really bad time," Karanka told a press conference.
"For those of us who have kept faith in him, seeing the look of happiness he has had on his face for a while now is very satisfying.
"A great player like him, and considering what he has been through, deserves to be happy again."
Kaka scored as Madrid defeated Ajax 3-0 in the Bernabeu last night.