The apology comes after church officials last month branded Sony's use of the cathedral as "beyond belief and highly irresponsible".
Following a meeting with the church, Sony admitted offending the cathedral congregation and the wider community. Sony has taken out a full page advert in the Manchester Evening News expressing its regret over the incident.
"It is clear to us that the connection between the congregation and the cathedral is a deeply personal and spiritual one," said Dr David A Reeves, president of Sony Computer Entertainment Europe.
"As a result, it is also clear that we have offended some of the congregation by using the cathedral in our science fiction game.
"It was never our intention to offend anyone in the making of this game, and we would like to apologise unreservedly for causing that offence, and to all parts of the community whom we might also have offended."
However the church is not entirely satisfied with the apology as Sony has not pulled the game, nor has any donation been made to the anti-gun crime movement, as stipulated in its original letter of complaint.
"We asked Sony to apologise unreservedly to the Cathedral and wider community for the offence caused. This they have done," said Dean of Manchester the Very Reverend Rogers Govender.
"We asked them to withdraw the game. They have refused to do this. We asked Sony to make a donation to community groups nominated by the Cathedral. They have not responded."
The cathedral has also released a set of 'sacred digital guidelines' aimed at video game developers and retailers, urging them to avoid violent games. The Digital Guidelines code of conduct is as follows:
1. Respect our sacred spaces as places of prayer, worship,
peace, learning and heritage
2. Do not assume that sacred space interiors are copyright free
3. Get permission from the faith leaders who are responsible for the building interiors you want to clone
4. Support the work of those engaged in resisting the culture of gun crime and those involved in promoting the work of conflict resolution
Buyers can demand refunds if they've had a game for no more than 14 days and not registered more than two hours of play
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