Speaking after Real's 2-0 win over Celtic in Philadelphia, Karanka spoke of the "competitive" nature he feels the squad have.
"We're very competitive, and always feel the need to express the best in ourselves. Once the championship returns, we're going to start showing people just how competitive the team is," said Karanka.
"With the players we have in our team, it is so much easier to work and achieve something together."
"There is plenty of unity in a group that is getting to know each other. The players are ambitious, and want to continue having success on the field."
Real begin their defence of La Liga against Valencia on August 19.