Juventus overturned a 2-0 first-leg deficit with a 3-0 second leg win over Atletico in the previous round and, although a goalless draw will suffice this time after last week's 1-1 draw in Amsterdam, Allegri was under no illusions.
"The first leg result counts for nothing," he told reporters, adding that Juventus needed to improve on their display in Amsterdam.
"We need to be more lucid with our passing and we need to be more accurate in building attacks which we did less well in Amsterdam, and we must show great respect for Ajax.
"We must also show the same intensity we showed against Atletico Madrid... If we do those things, we can progress to the next round."
Ajax have played seven away games in the competition this season, including the qualifying rounds, and are still unbeaten on the road. In the previous round, they won 4-1 at Real Madrid after losing 2-1 at home.
"We will need to understand the different moments of the match. Ajax played better in Madrid than they did in Amsterdam and they have not lost away," he said.
"We must do well attacking, be focused in midfield and when we defend. It will be very open, we need above all a great performance, both physically and technically."
Allegri confirmed that forward Mario Mandzukic would miss the match through injury and that veteran defender Giorgio Chiellini was also ruled out.
(Writing by Brian Homewood, editing by Pritha Sarkar)
