Hart made a string of fine saves to restrict Dortmund to just one goal and the point was won through Mario Balotelli's late penalty.
England goalkeeper Hart admitted that City were outplayed and that the team are "happy with a point".
"We've got to be happy with a point," Hart said. "It could have been 10-all today.
"I don't know if it was a penalty but Mario was not going to miss that. We kept ourselves alive in the group. I thought Borussia Dortmund were different class tonight."
City are currently third in Group D, five points behind leaders Real Madrid.