With Milan ahead of their preseason friendly against Arsenal in Singapore, Tomori branded last season as "horrible".
He told local reporters: "Last season obviously wasn't a good one. We obviously want to do better, we're working hard and preparing for next season. We're very happy to be able to play matches here.
"Every coach has his own ideas on how to defend, how to attack, how and when to press. We're adapting to Allegri's requests.
"Last season was horrible. The feeling is different from last season, and we want to be ready to get good results. We want to return to the Champions League, a competition where Milan should always be."
Tomori added on facing Arsenal, "I know English teams well; they're tough to play against, and they're a good team. But we want to do well in every match, preparing well for the game and for the upcoming season.
"We're ready for the first test. We arrived last night with a lot of fans to welcome us. We're pumped for this match."