I don't think this is a big mistake for Napoli, because Spalletti also wanted to leave.
Leaving after winning that trophy is far better than stay with club a few more seasons and failing to get the title. Maybe Spalletti also thought of this, as we know, there are several coaches who take the same way. Zidane for example, he came out as coach of Madrid after get the title, as far as I remember Rijkaard did the same (CMIIW). Of course going after get the champion title will get a positive impression.
Actually, Spalletti have personal reason why leaving Napoli after success winning scudetto last season although Napoli have impressive performance not only in domestic league but also in Champion League. Spalletti has good reputation although leaving Napoli because he won tittles before leaving teams and the same did by Zidane after success with Real Madrid. But problem for Napoli will be success for defending their domestic league tittle next season after leaving by many key players and Kim Min-jae has leaves Napoli for joining Bayern Munich.