The race fell out of the Reds' hands when they suffered a 2-0 defeat to Chelsea last Sunday.
Manchester City are now favourites to clinch the trophy as they have a game in hand, but Barnes has urged supporters to stay hopeful.
In an interview with talkSPORT, Barnes said: "What the Premier League has shown me this year is that anything can happen, so while Liverpool supporters might feel down and out they certainly still have a chance, but it's not in their hands anymore.
"I expect them to win their last two games, but for me to say I think Man City will drop points will be hopeful more than anything."
Liverpool will take on Crystal Palace and Newcastle United in their final two league games.