The 46-year-old has stressed the importance of picking up three points in Amsterdam on Tuesday to avoid having to beat the Blaugrana
The Serie A outfit beat Celtic 2-0 win in their first match of the group stage, but travel now to the Amsterdam ArenA where they have won just once in four trips.
With Spanish giants Barca drawn into their group, Allegri knows every point is crucial if they hope to advance to the knock-out stages.
"Ajax are a very intense side, a bit like PSV where we struggled a lot in the first few minutes [in the qualification phase]," he told reporters.
"We have to do well in these situations, there is a lot at stake. A victory would allow us to go into the Barcelona game with a relaxed approach.
"In the league we have to pull our sleeves up but tomorrow we need to approach the game with a lot of focus and a good deal of skill."
Allegri will have a well-rested Mario Balotelli available for selection, after missing the club’s previous two matches due to a three-match suspension.
"I think Balotelli is relaxed, he just has to think about playing football, he has to learn to have respect for other players and for the referees.
"For now I have Balotelli available and I will as well after the international break."
Stephan El Shaarawy is unavailable with injury and does not make the trip to Amsterdam, along with a few other first team regulars, but Riccardo Montolivo and Riccardo Saponara are fit and available for Tuesday’s match.
"We are very unlucky at the moment. Up until now Milan’s injuries have been 80 per cent trauma injuries and only a wizard knows why the rest are muscular injuries.
"If I had known that El Shaarawy was going to get injured I would not have made him train.
"Montolivo and Balotelli are important players. It is a shame about El Shaarawy, that he isn’t here. Montolivo is the captain and his return is important to us and Balo is also very important for us and he has to show that tomorrow.
"My form is mirrored by that of the team, it is improving. If I look at the results in the league then I know we can do better. We have to do our best to win the game tomorrow."
Milan sit ninth in Serie A after six games and European football will be a welcome respite to a rough start to domestic football in 2013-14.