The England international was not part of the 18-man squad for the goalless draw at Stamford Bridge.
It was the fourth time Abraham had not played in February, and Tuchel admits the 23-year-old is unhappy with the situation.
"Selection. We have 21 strong players and only 18 possible [to be picked]. It is my job to take hard decisions. This was the decision for 18 guys and Tammy was not with the group," he said.
Tuchel added at his post-match press conference: "At the moment he is only struggling with my decision. We have a strong squad. We have only Thiago Silva injured that means we have to make hard decisions.
"We can nominate 18 players, plus goalkeepers so it is clear. It was also an unfair decision for Billy Gilmour because Billy played well in the cup and he was very strong in training.
"It was a hard decision. It was about judging the alternatives that we have and we opted for Olivier Giroud to begin, Timo Werner on the bench. We have Kai Havertz who can play as a number nine so there was no need to bring a fourth number nine to the pitch.
"Things are difficult for him. Things are not as easy as they should be for him in the moment and he will get full support. This was the decision."