The Rossoneri boss has endured a torrid start to the new campaign, losing an alarming five from eight league games so far and struggling to register points on the continent.
But ahead of Saturday night's visit of Genoa, Milan vice-president Adriano Galliani insisted Allegri is the man to rebuild the club, with the full backing of president Silvio Berlusconi.
Allegri told Gazzetta.it: "I've never feared the sack, even given the hard times we are going through.
"We are giving our all to climb up the league table and to progress in the Champions League.
"We have to persevere, improve and be a bit more clinical in front of goal.
"The boys have quality and I'm convinced that will see us through.
"Tomorrow will be an important game because we want to give something back to the fans.
"Hopefully that will be the victory that the players deserve for what they have done on the pitch."
Veteran manager Luigi Del Neri takes control of the Grifone for the first time after replacing Luigi De Canio this week, and Allegri is wary of what the Ligurian outfit have to offer.
"They're a good team, who have good technical players and a coach who puts a lot into arranging his defence," said the 45-year-old.
"Our responsibility is to stay patient and not let ourselves down by being too anxious.
"We have to go onto the pitch knowing that we have 90 minutes to secure the win - without being nervous and panicking.
"We have to play a simple game. But we absolutely have to win, and the boys are in good enough shape to do so."
One player who is not in good enough condition to take part is Holland international Nigel De Jong, who is struggling with a hip injury.
Del Neri might have preferred a simple debut in the Genoa hotseat, and his cause is not furthered by the loss of striker Marco Borriello (ankle) for six weeks.
At his unveiling, the former Chievo boss said: "There is every chance that we can be successful.
"We want to start laying the foundations for years to come.
"We won't overhaul everything straight away but we do need to change the road we are going down."
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.