Allegri is one of the top coaches in Europe. He is tactically flexible having used three main formations at Juventus, the 3-5-2, a narrow diamond and in his final season the 4-3-3. Allegri deserves more credit than he gets, Juventus continued to dominate domestically under his watch, whilst also finally showing their potential in Europe. Allegri is also the last manager to win the title with another giant of Italian football AC Milan whilst also having the best win percentage of any Juventus manager.
Allegri is a manager who builds tactics around the players available to him, in contrast to other managers who buy specific players for their system ala Guardiola. Allegri was able to continually rebuild his Juventus sides whilst still winning year after year domestically and challenging in Europe replacing key players like Pirlo, Buffon, Vidal & Bonucci without spending huge transfer fees.
With the ball like many coaches, he likes his teams to play from the back retaining possession to move up the pitch. However, his teams are also comfortable playing more direct if required. Allegri also instructed his teams to always look for the killer ball rather than playing the safe pass. His teams would use countermovements in the final 3rd to open up space which would then be exploited ruthlessly. by either Morata or Tevez.
Defensively, Allegri would set his side up in a 4-5-1 or 4-4-2 shape. Allegri stresses the importance of holding a compact block without the ball, Juve would often sit deep in defensive situations preferring to defend from the edge of their box, limiting space in behind and making them difficult to break down.
Therefore Juve would not employ an all-out counter-press, they would instead retain a solid shape and press as one compact unit. Using a midfield cover shadow to protect against through balls played centrally, forcing their opponents to the wider areas of the pitch.
Check out the video below for a full breakdown of the tactic used by Allegri.