The Nerazzurri got back to winning ways against the promoted side but the former Napoli boss was critical of his players, and Ishak Belfodil in particular
The resurgent San Siro outfit were always in charge of proceedings, but their reckless approach presented their visitors with numerous opportunities to get back into the game.
Mazzarri has laid down that his men should be more results-oriented, urging them to remain concentrated at vital junctures of a match.
"We're a young team with lots of lads who aren't used to having the responsibility of playing as starters and having to win games," the former Napoli boss ranted afterwards.
"We got off to a superb start, got into our stride and even started trying things that were more to please the crowd than find a route to goal, and that's not something we should be doing.
"Then we made a few mistakes that could have been avoided and we let Verona back into the game. If we want to challenge at the top then we can't afford to get distracted like that.
"After the break we went back out there looking good and scored another, then our attention levels dropped again."
Ishak Belfodil came on in the second period but bizarrely received his marching orders after the final whistle following an altercation with Evangelos Moras.
"Belfodil goes from the fantastic to the naive. You have your top players and then you have others you need to help become top players," Mazzarri chided.
"I think it's about being mature: regardless of what anyone says to wind you up. Having said that, I don't think it warranted a red card. The game was already over."
Nevertheless, the former Napoli trainer had words of praise for Rodrigo Palacio and Mateo Kovacic, the latter receiving a rare start.
"Palacio is an established star. Rodrigo had a great season last year and this year he's doing even better," he concluded.
"Kovacic was playing in new position and he did well, especially when we broke forward the way we were supposed to."