The Reds have failed to net in their last three Premier League matches - their longest such run since another three-game spell in March 2005.
Thiago has played a part in all three of those games and started two of them, including Sunday's 0-0 draw with league leaders Manchester United.
Barnes believes that the Spanish midfielder, still working his way back to fitness following a two-month layoff, is too slow in possession.
"Thiago, who was running the game and was the best player in the first half, I don't think that necessarily helped the front three," he told talkSPORT.
"With [Jordan] Henderson and Fabinho in midfield, they just get the ball forward and are much more direct for the three strong-running strikers to get on the ball and go on attack, Thiago slows the game down.
"When he slowed the game down in tight areas, that is not [Sadio] Mane's game, that is not [Mohamed] Salah's game. So we're getting used to a new system, but at the moment it's not working.
"But in my opinion, along with Manchester City, we're still favourites [for the title]."
Liverpool have found the net just once from their last 62 shots - 17 of those efforts against United, who retain a three-point lead on the fourth-placed Reds. body check tags ::