The loss sends Catania to bottom of the Serie A table.
But new coach Mihajlovic said: “I cannot reprimand my players for anything, as they gave it all they had and Livorno won the game with their only shot on target.
“I have worked more on the mind of our players. We had three or four excellent scoring opportunities in the first half, but did not take them and this is how football works.
“When you don't make the most of your chances, it can happen that your opponents score with their only shot on target.”