The Japanese club needed to overcome their Chinese counterparts to stay alive in the competition but were unable to do so, going down 2-0.
Takahata was full or superlatives for Beijing who took second place on the Group E table to set up a knockout clash with Korea's Suwon Bluewings.
"My players have done their best. Frankly, I think Beijing is a wonderful team," he said.
"It was really difficult to beat them, particularly in an away game.
"Their defence played very well. Since we had to win all three points, we could focus only on offence, but Beijing's steely defence kept us at bay."