The Heysel Stadium disaster saw 39, mostly Juventus fans perish when they were crushed against a collapsing wall as they tried to escape rampaging Liverpool fans prior to the European Cup final on May 29th 1985.
Juventus won the final 1-0, although their victory has long been overshadowed by the widespread belief the final should never have been played.
By a twist of fate, Juventus will appear in the final of Europe's premier club competition this year when they face Barcelona to decide the destination of the Champions League trophy next week in Berlin.
Allegri will lead his side into their final game of the season, away to Verona on Saturday, hoping to finish on a high having already secured their first league and Cup double in 20 years.
But the coach said: "Today all we should be thinking about is commemorating the victims.
"We have to make sure something like this never happens again. Football, as a sport, is a show and the show should never be hijacked by violence and vandalism."
Allegri and Juventus staff are set to participate in a remembrance mass in Turin on Friday evening at the Gran Madre di Dio church before leaving for Verona.
Although Juventus could finish with a 16-point cushion on league runners-up Roma, Allegri said he is not taking their last game of the season lightly.
"It will be an important game for us as it's our last outing before we play the Champions League final," added Allegri.
"We're in good physical shape. We need to go to Verona with our heads completely focused on this game so we can finish the league season the best way possible."
Mid-table Verona have escaped relegation and failed to qualify for Europe, but the season is far from over for Verona's evergreen striker Luca Toni.
He sits top of the Serie A scoring charts on 21 goals, one ahead of both Juve striker Carlos Tevez, and Mauro Icardi, whose Inter Milan side host Empoli on Sunday.
If 38-year-old Toni finishes top of the pile, he will become the oldest winner of the league's 'Capocannoniere' (top scorer) award since Piacenza striker Dario Hubner, then aged 35, shared the prize with Juve's David Trezeguet in 2002.