Milan endured a poor campaign in Italy's top flight last term, eventually finishing in eighth some 45 points adrift of champions Juventus.
The San Siro outfit therefore missed out on UEFA Champions League and Europa League football for the coming campaign.
Milan also performed poorly on their recent tour of the United States, Filippo Inzaghi's men losing all three matches in the International Champions Cup.
However, De Sciglio is unconcerned and expects Milan to challenge in the league given the amount of time they will have to prepare for fixtures.
"We all have a great desire for revenge - this year we only have the league so we will have the whole week to train well and be ready on Sundays," he told Milan's official website.
"The US tour? We didn't get good results, but against Liverpool we were more solid and compact as a team compared to the other matches.
"We want to go out onto the pitch and play our game, as the boss wants. I think we will have a great season."
De Sciglio picked up a knock in the 2-0 defeat to Liverpool last Saturday following a collision with team-mate Gabriel.
The full-back revealed the issue is not serious, although he could miss two weeks of training.
He added: "These things happen, he [Gabriel] had to go for the ball. It was a tough challenge, but I repeat, these things happen.
"It's nothing serious, it will need around two weeks to recover. Every day that passes things are going better."
