Ahead of Saturday night's trip to face Serie A title hopefuls Roma, the Nerazzurri are 26 points off the pace set by leaders Juventus and 11 behind Napoli, who occupy the last Champions League place.
New owner Erick Thohir expects Mazzarri to guide the club back into the Europa League after a season without continental action, but Inter risk losing their grip on fifth place with Hellas Verona and Parma both looking upwards.
Victory at the Stadio Olimpico, where they have failed to win a league game against Roma since 2008, would go a long way towards boosting morale.
But, regardless of the outcome, Mazzarri feels he deserves longer to turn things around.
He told La Repubblica Sport: "We need time because Inter are in a period of reconstruction, with many new players and a new coaching staff. There's also been a change of ownership.
"With all these changes, we definitely need some time to work on getting things back to normal.
"A club like Inter should only be concentrating on the hitting the highest targets and I am confident that, with a little bit of time, we can do that."
On-loan Porto defender Rolando, who scored his third Inter goal in last week's 1-1 draw with Cagliari, echoed Mazzarri's comments and stressed the importance of securing a return to European competition.
He told inter.it: "A big club like Inter should always aim high but this is a year of transition, because last year was very difficult.
"The least we can do, however, is to get into Europe.
"It will be a difficult game against Roma but I don't fear anyone or anything, even though I know they're a great team that are having a great season.
"But if we can do things properly then we'll have a good game."
While Hugo Campagnaro is the only player on Inter's treatment table, Roma are seriously struggling for numbers with Dodo, Federico Balzaretti, Maicon, Alessandro Florenzi and captain Francesco Totti all out injured.
Despite the personnel crisis, Giallorossi boss Rudi Garcia remains confident his squad has enough strength in depth to keep chipping away at Juve's nine-point advantage.
He told asroma.it: "We're having a magnificent season.
"The guys have to understand that they must give everything they have when they're on the field and think about the good of the team.
"We need everyone to chip in, especially at times when we're finding it hard.
"We have to give 100 per cent defensively: that's not always easy when you're feeling the fatigue but it's something we have to do."