Kane was named on the bench for the game at Wembley Stadium, but two first-half goals meant that the England international could watch the 2-0 win from the sidelines.
The club's top goalscorer suffered with illness over the Christmas period, and Pochettino has acknowledged that he had been keen to hand the player a break before Saturday's North London derby with Arsenal.
At a press conference, the 45-year-old told reporters: "Yes, it's important to have all the players fresh.
"Of course with him, in a very short period, he suffered two illnesses and it's important to care about him. He was fantastic with plenty of energy and then he got a cold, and dropped his energy.
"For me yesterday it was so important to keep him away from the game to provide better energy for the next few games."
Kane has netted a total of 31 goals from 32 appearances in all competitions this season.