Doorkins took up residence at the cathedral in 2009 and became a much-loved member of the cathedral community until her retirement from official duties last year.
She died last month at the home of the cathedral verger who she had lived with in her final year.
Introducing the service – which was streamed online – the Dean of Southwark, the Very Revd Andrew Nunn, said: "This church ... will have seen many things celebrated and people remembered.
"We host – in more normal times – memorial services for the great and the good, and the funerals of our neighbours, our friends and our family.
"But I suspect we've never had a service for a cat. I know some think it's strange that we should be doing this, perhaps even wrong.
"But – as we will remember in this service – every part of creation is in the sight of God, the creator, the sustainer, the sanctifier- not just of humankind, but of all that God placed in the garden of God's delight."
The Dean added: "Some may think the cats don't deserve ceremonies and eulogies and prayers; that their death should pass without comment, or occasion. But I can't agree. And I'm not particularly a cat person, or at least I wasn't before I met her.
"But this little cat who arrived at our door, who chose us and stayed, changed our lives and enhanced our mission and ministry.
"She did more to bring people to this place than I will ever do."
At the end of the service Doorkins was buried in the cathedral churchyard.
News of the service caused controversy in some church circles on social media. The Bishop of Burnley, the Rt Revd Philip North, said that it was "grossly insensitive to bereaved families and those ministering to them in the North West under the regional Coronavirus restrictions".