The Inter boss has issued a riposte to the Fiorentina coach following criticism earlier this week, but was left to rue his side's inability to take maximum points at Cagliari
Montella claimed the Nerazzurri coach would become "offended" if his side were earmarked as title contenders given the high wage bill at Giuseppe Meazza, while he accused the former Napoli boss as being "good at complimenting teams before games, but not after them" after their 2-1 win over the Viola on Thursday.
Speaking after his side's 1-1 draw with Cagliari on Sunday, a visibly-irritated Mazzarri told Sky Sport Italia: "Perhaps Montella was wound up and just wanted to make himself look calm.
"I said Fiorentina are one of the Scudetto contenders after the game, so how is that not a compliment?
"In the last two years Inter have dropped their wage bill from €180 million to €80m, which is the opposite of what clubs like Fiorentina are doing. That has to be mentioned if we’re analysing the maths of who is pushing for what.
"Montella was wrong, but he just kept on going. Nobody talked about Fiorentina. I’d have more to say to Montella too, but I’m not going to do it here."
A deflected Radja Nainggolan strike in the closing stages denied Inter a win in Sardinia on Sunday and Mazzarri was frustrated to see his side unable to take home maximum points from the encounter.
"The lads started very strong despite the heavy pitch and we probably deserved to take an earlier lead. It’s a shame to have played so well and taken home so little," he said.
"The goalkeeper was in great shape today and saved everything. We were also a bit slow and sluggish in front of goal, and one chance got stuck in a puddle. It seemed like the first half against Sassuolo, only without the ball being in the net.
"When you talk about fighting for the top of the table, anyone who has been there knows that if you play great football and don’t put it in the net, then you go nowhere.
"Cagliari are a strong side with a midfield barrier in front of the defence, so we knew that we’d have to keep possession and then inject a sudden burst of pace."
Inter remain unbeaten with four wins and two draws from their opening six games, but Mazzarri remains wary of any premature talk of a title push.
"If someone says this team can get the Scudetto and we finish second, it’ll be seen as a failure," he added.
"What really counts is how we play on the pitch and build a series of good results. At least wait until the midway point of the season before giving an opinion on where we are and what we can do."