Keegan says in tomorrow's official programme: "Of course our home results need to be better. Three wins out of 15 here is simply not good enough.
"It is no good me arguing that the performances have deserved better when the reality is that our poor home results are responsible for our predicament. Yet our goal difference is far better than that of the other sides in trouble."
He adds: "We can do it at home because we have three games left here and three wins will see us in the clear. But I don't want us having to go to the last game of the season, against Everton, still needing something to stay up.
"I want the job done as quickly as possible. It will not be achieved without a good deal of sweat and some nervousness because footballers are human beings and we find ourselves caught up in a dogfight."
The City boss believes City are worthy of Premiership status, saying: "We have to stay in the Premiership because we deserve it, our supporters deserve it and our stadium deserves it. Our players are good enough but they still have to make it happen."