The former AC Milan playmaker was at his sparkling best at the Bernabeu as Jose Mourinho's side, who had opened their Group D campaign with a hard-fought 1-0 victory over Dinamo Zagreb, eased to the three points against the Dutch champions.
"Kaka has, frankly, had a rough time," Karanka said on www.realmadrid.com. "He is a quality player and it is very important for us to see him happy and enjoying himself because it means he will be an essential player on this team.
"He is the first one who deserves to be fit. The rest of us simply have to stand by him and support him."
Karanka was also full of praise for midfielders Xavi Alonso and Mesut Ozil.
"Having Alonso, Kaka and Ozil together on the pitch was different," he said. "On Saturday [6-2 Primera Division win over Rayo Vallecano] they all played in midfield. Tonight Ozil played closer to the wing. A quality player like him adapts to anything."
As well as Kaka, Cristiano Ronaldo and Karim Benzema were also on the scoresheet last night.
The latter was substituted in the 75th minute due to injury, but Karanka played down concerns over the severity of the knock.
"Benzema said he was feeling some pain and we'll see how that evolves," said Mourinho's number two. "We didn't want to take risks, but it doesn't seem to be anything serious."
He added: "We wanted to put pressure in attack at times and also in defence.
"You have to use your skill at making that transition when you face a side that keeps so much possession at the start of the match.
"It's true we allowed Ajax to have more possession after scoring our third goal, but we never experienced danger."