Rice is serving an indefinite suspension from the NFL after the release of a video that showed the running back knocking out Janay Palmer with a punch.
The NFL and Ravens claimed they first saw the video when it was released by celebrity website TMZ in early September.
Speaking to reporters on Monday, Bisciotti said he was sorry for not doing more to get access to the video sooner.
"There is no excuse for me to have not demanded that video except I wasn't concerned or interested enough to demand it, never crossed my mind," he said.
"I'm sorry for that, deeply sorry for that."
The media conference was called to address a report on ESPN, with the Ravens issuing a 15-point rebuttal.
Rice, who was initially handed a two-match ban, is appealing his indefinite suspension.
Bisciotti said he should have demanded access to the video.
"If it would have crossed my mind, I would have demanded it (the video)," he said.
"If I had demanded it, I would've gotten it... I would have forwarded it to the NFL."