Gennaro Gattuso left the Italy job on Friday after his side's World Cup playoff loss to Bosnia on penalties - a third straight missed qualification for the four-times champions, with federation (FIGC) chief Giuseppe Gravina also stepping down.
There were plenty of questions regarding Italy's failure and Allegri's own future at the press conference ahead of Monday's Serie A game at Napoli.
"As an Italian, I'm very sorry about the failure to qualify, but we must take it as an opportunity for growth and have a strategic vision for the next 10 years," Allegri said.
"Making judgements and saying what should be done... I believe that there are the competent bodies that must meet and examine the rules, from the grassroots activity to the first team."
Allegri made his return to the Milan bench last year, having won the Scudetto in his previous spell, and in his first season back his side are second in the standings, six points behind Inter Milan and one ahead of Napoli.
The 58-year-old, who won five league titles at Juventus, was asked if he would rule out coaching Italy, now or in the future.
"I started a journey last year with Milan, now we have to be focused on finishing the season well and reaching the Champions League," Allegri said.
"I haven't thought about it yet. I'm fine at Milan and I hope to stay at Milan for a long time.
"It's been a few years since I have taken part in the Champions League, if we were to qualify and I were still Milan's coach, I'd have to get used to it again."
Allegri was questioned as to why he had used the conditional when speaking about his Milan future.
"Life is unpredictable, you never know what can happen," Allegri said with a smile. "First, let's try to arrive in Champions, and then we'll see."
The top four qualify for the Champions League and Milan have a nine-point cushion over fifth-placed Juventus with eight games remaining.