The Reds were clear at the top of the table before being undone by Jose Mourinho's side at Anfield, which allowed Manchester City to close to three points behind with a game in hand and superior goal difference.
Manuel Pellegrini's men were made favourites with bookmakers as a result of their win at Crystal Palace but Keane argues that Liverpool remain "in a good position" if they can stay mentally strong.
|5/4||Liverpool are 5/4 with William Hill to win the Premier League|
"They're not out of it yet. They're still in a good position. I wouldn't write them off.
"At the end of the season, it's not just physical, it's a head job too. You have to be in the right mind."
The former Manchester United star said on Tuesday that some of his old club's players should be "ashamed of themselves" for their role in the sacking of manager David Moyes but, though reiterating that the Scot deserved more time, Keane says that he is not too worked up by the decision.
"I made my point last week about Moyes," he remarked. "I feel sorry for David. I thought he should have been given more time.
"Whatever is going on at certain teams is really none of my business. I look at David Moyes, I don't like what's happened to him but, regarding other clubs, it's none of my business and doesn't keep me awake at night."