The Nerazzurri boss was frustrated as his side struggled to break down a dogged Chievo side on Monday but stressed his plan with the team remains a work in progress
The Nerazzurri have failed to win any of their three games in 2014 and were forced to settle for a point against Chievo after Yuto Nagatomo equalised Alberto Paloschi's early goal.
New owner Erick Thohir earlier stressed that fans should not expect any stellar arrivals in January as he looks to rebuild the squad and Mazzarri echoed the Indonesians' plea for patience.
"I have to compliment the new president, as few would say those things openly. I hope the fans have patience. I already knew all this, but I was pleased we are all on the same page and are working on this project," Mazzarri told Sky Sport Italia.
"First of all, to buy someone we need to sell first. A coach tries to do his best with the squad at his disposal. I work on Ricky Alvarez and Mateo Kovacic to ensure they cover each other when changing position. All this means growing up, gaining experience and learning the tactical moves."
Looking at his side's draw with Chievo, which sees them sneak back into the top five in Serie A, Mazzarri made it clear he was more than happy with the team's endeavour.
"I could not have asked for more from my team. We knew Chievo were organised in defence and physically strong, but we had a great chance with Rodrigo Palacio," he told continued.
"If we had taken the lead, then it would've been a more entertaining match with more open space. We know that to play good football it takes two teams, but Chievo came here to defend and hope for a mistake to hit us on the counterattack.
"I changed system tonight, as I wanted to help the lads find some more spaces with a 3-4-3 system. We did create some scoring opportunities, but missed the final ball and Mateo Kovacic got between the lines but didn't get the right pass.
"Sometimes the ball just doesn't go in and your opponents score with every shot. You just have to keep working. The boys believe in themselves, we just need a little more luck, which is crucial in sport.
"For various reasons we have fewer points than we deserve to have. If it's our destiny we'll get them back before the end of the season, but if not then we'll just have to see where we end up."
AC Milan parted company with Massimiliano Allegri earlier on Monday after a disappointing first half to the season and Mazzarri stressed that supporters should rememebr the success Allegri brought to the club during his tenure.
"The coach always pays. A coach going towards the end of his contract is always going to have every result weighed heavily on his shoulders. I just hope people remember all the good work Allegri did, as they forget so quickly in football," he added.