"Llorente wasn't depressed at not scoring yet this season, but it's normal that a goal is important for a striker, even if he likes to play for the team," Allegri told Sky Sport Italia.
"This was the right game for him, both for his physical characteristics and to let Morata rest. I am happy he scored, as he repaid the faith we have in him and above all his own self-confidence.
"It was a poor first half and Palermo made it difficult for us, but we increased the tempo after the break and did better."
Juventus remain unbeaten in the league and the win restored their three-point lead over Roma at the top of Serie A.