Empoli were beaten 2-0 at home as Milan struck through Rafael Leao and Santiago Gimenez.
D'Aversa said afterwards: “We saw a real deficit of experience between my lads and the Milan players this evening."
Luca Marianucci was sent off for striking Gimenez in the second-half.
D'Aversa continued: “Gimenez was sneaky, but then when I hear any player described as ‘sneaky’ then I start to think something is not quite right.
“We have also had a lot of injuries and the performances have been good, including today against Milan. The only time we really got it wrong was 20 minutes against Lecce. I know it’s a bad habit in Italy, but I don’t like people judging based only on results and not taking the performances into consideration.”
On his words to AC Milan counterpart Sergio Conceicao at the end, D'Aversa added: “I congratulated him and he did the same to me, but then I also told him it’s not right to systematically call the fourth official and referee. It was in the heat of the moment and nobody likes to lose.”