Despite rivals United winning their last six league games to climb within two points of leaders Leeds, Keane insists their chances are still limited.
The Republic of Ireland midfielder said: "I still think they are better placed than us if you look at the points we've dropped.
"We've got to go to Leeds and Liverpool and Arsenal have got to come to Old Trafford but we really can't afford any slip-ups.
"I think Arsenal and Liverpool have games in hand, so I think they are in a better position."