The result has opened up a five-point gap from Inter Milan and this could hit morale.
"I don't think my players are frustrated by the fact Inter always manage to win," insisted Spalletti. "We are a team who always want to play open football and that inevitably gives our opponents chances to score.
"The pitch was heavy from the rain and did not allow us to move the ball around as quickly as we usually do. Livorno are a tough side to face."
Francesco Totti was also disappointing on the day after returning from his five-week injury lay-off.
"A player like Francesco needs the movement of the squad to create space. When that doesn't happen, there will be more problems."