Allegri braced for key Olympiacos clash
The Italian champions sit third in Group A after three games and suffered a surprise 1-0 defeat to the Greek side last time out in Athens.
Trailing Atletico Madrid and Olympiacos by three points going into Tuesday's fixture at the Juventus Stadium, Allegri's men have work to do if they are to ensure progression from the group stages, having bowed out in third place last year.
"It's an important test against a team who play decent football. We need to tackle it with plenty of focus and intensity," he said.
"Anything can happen in football, but I think [this] game will be decisive as far as our Champions League destiny is concerned.
"We need to improve on our display in Athens. We were sloppy with our passing in the first half.
"We need to make the most of all the time we have to get the right result."
Despite dominating domestically in recent seasons, Juve have yet to translate that into European success.
In his first campaign in charge at the Juventus Stadium, Allegri dismissed suggestions there was now a "complex" at the club surrounding continental competition.
"We need to look to win and do so by a decent margin if possible," he continued.
"There's no European complex here, but we do however have three points on the board and need to put this right.
"We need plenty of positivity from ourselves and the fans. The lads are more than capable of winning this game."