The 45-year-old did not have the best of campaigns in charge at San Siro last term, as Milan fell behind the pace of title winners Juventus before being beaten by them in the quarter-finals of the Coppa Italia and losing to Barcelona in the UEFA Champions League last 16.
Their disappointing third-placed Serie A finish is something Allegri is keen to improve on, and he is confident his squad can challenge for the title next term.
"Compared to last year, the AC Milan players already know each other since they have played together for a year," he said.
"We still have room for improvement and we should keep on working hard, as we have done in the last year. We know that things are getting trickier this year.
"In addition to Juventus, which is the favourite team to win the championship, there are also six other teams, which will be battling to achieve a Champions League and Europa League spot."
Allegri has so far brought in several key signings ahead of the new campaign in the shape of Andrea Poli, Cristian Zapata, and Jherson Vergara and he admitted that he expects to see more movement in the transfer window, although most of it will be leaving the club.
"We've got 25 players in total plus a few players who will be leaving," he continued. "This is the number of players who will make up this year's squad.
"As we have already said, we don't want a squad made of 30 players. If some players will be leaving, they will be replaced by other players, otherwise this will be this year's squad."
Allegri has also backed Stephan El Shaarawy to find his form again after struggling in the second half of last season - the Italian has only scored twice in 2013 but his manager knows he has the ability to lead the Milan attack.
"I still haven't talked to (Stephan) El Shaarawy," he added. "He needed a break, he is only 20-years-old and he has found himself under a very high pressure from the media.
"Therefore it's normal for him to want a break in order to recharge his batteries and find the serenity he may have lost in the last part of last year's championship because he didn't manage to score a lot of goals.
"But despite this, his performance on the pitch has never decreased because he has always been very useful and willing to help the team."
