Boro have the fourth worst defensive record in the Championship this season, conceding 26 goals in 16 games.
Karanka told BBC Sport: "No, we have not been concentrating on our defence. I was a defender and we never trained like that, attack as a team and defend as a team.
"Our attitude was good against Leeds, but we must improve our concentration to make less mistakes, not put extra focus on the defence."
Boro were beaten 2-1 by Leeds United in Karanka's first match in charge last weekend.