For me its not a problem he said what he said, when questioned, constantly, about it the response was pretty simple. He's trying to appear confident of the task at hand, so his players don't get the impression their manager has no confidence in them.
Thats fine, I don't care that he lied, though telling everyone he was basically just lying to try to keep the squad together, is basically the same thing as saying in reality, he doesn't have confidence in those players, which just makes him a bit of an idiot. You can't pump up players confidence by making a statement, then explaining the statement was basically not what you believed anyway.
City are what 6 ahead now, with a game in hand, so if thats 9 points, Liverpool have 4 games left and a 9 point gap, its incredibly unlikely isn't it, they've also scored less and got a worse GD so they'd need a clear points advantage thanks to a couple demolitions of poor teams by City. One win, or two including the game in hand out of 5 could pretty much seal Liverpools fate.
4th is still well up for grabs, if City, Spurs and Villa all win their games in hand the current table would be City with 65, Spurs with 64 and Villa with 60, Villa with a horrible goal difference. If City/Spurs drop a game and Villa win theres, they are right back in it.
As Liverpool or a possible 6 points of 6th place when all the games in hand are sorted out, they are screwed.