Pochettino confirmed upon arriving at the Ataturk Olimpiyat Stadium that it was a family-related matter and that the striker had requested permission to return home.
"When you have a problem, your mind is not quite... it is a difficult to give your best," the Spurs boss said.
"I have always told you that players are human. Many problems happen and it is important to fix this type of problem because always family is important.
"But we hope when he comes back he will be ready to start training and to help the team."
Pochettino rejected talk Adebayor could be absent throughout the Christmas period and went as far as suggesting there was a small chance he may be back for this weekend's trip to Swansea.
The former Argentina international admits that is unlikely, but played down the impact his absence could have over the hectic festive period.
"Yes, it is an important time but we need to understand that the players are people," Pochettino said.
"They need to fix when family matters happen and you need to sort it. If not, it is difficult to give the best.
"After, yes, we know we have ahead a lot of games. It is a very busy period, but the first [thing] always is if you are okay, if you are ready, if you are in your mind clear.
"When things like that happen, it is very difficult for the player and it is important. Maybe we lose three or four days in training, but you win a lot because if not the problem is always in his mind and it is difficult to break this cycle.
"Now, it is important that he takes time, sorts out the problem and when he is back is ready to train and be available."
