Manchester City returned to the top of the Premier League table on Sunday with a 6-0 demolition of Chelsea.
They are ahead of second-placed Liverpool on goal difference but the Reds do have a game in hand.
Liverpool were seven points clear of City ahead of their clash at the Etihad on January 3.
Barnes says his former side would have won the league if they won that match, but City ran out 2-1 winners.
Manchester City have won their last three matches, with victories over Arsenal and Everton before the Chelsea rout.
Barnes says Liverpool must focus on their own job but admits he would like a slump in City’s form as well.
“I’m not worried about the form City are in because we can do nothing about that,” Barnes told Sky Sports News.
“I would like to hope that City lose the next five games but it’s not going to happen and I’m not concerned about City.
“Had we beaten City to go 10 points clear I would have said we would have won the league.
“When we lost that game, I still made City favourites.
“As much as we’re doing really well and the fans and some of my friends are getting excited, I said ‘well listen, when you come to February, March, and you look at the size of the squads, City have got a bigger squad if people lose form, people get injured’.
“But we are still there, we can still go three points ahead of them if we win our game in hand.
“I still make City favourites to win the league but I think we will push them all the way and of course Liverpool can win the league.
“I didn’t get carried away when we were going to be 10 points clear and now I’m not going to get despondent like a lot of Liverpool fans because now City are on a rise and they think that we’re stuttering.
“We’re not, we’re still winning games, we’re doing well.
“So it’s going to all go down to the wire.”
Liverpool are now not in league action again until February 24 when they visit Manchester United.
City host West Ham three days later after they play Chelsea again in the Carabao Cup final.