Pietro Pellegri gave Empoli the lead before Santiago Periotti struck a second-half equaliser for Lecce.
Afterwards, D'Aversa said: “I think we did better for 60/70 minutes. We had the chance to double the score. When you don't close out matches you can suffer the episode like what happened with the goal conceded.
"In the end we can also consider ourselves lucky, but we had the chance to restart 4 against 2 that we could have exploited better. We had many absences, the boys played a great match. We know how much the crowd pushes here, we had ten minutes of suffering but I think it's normal."
On his return to Lecce, D'Aversa added: “I thought about the many beautiful things we experienced here. Matches like the ones against Fiorentina, Milan and Lazio will last forever. When I wasn’t coaching Lecce I stayed here to live.
"There were messages of solidarity despite what happened. When I think of Lecce I have so many positive memories, both in football and in my private life."