The Rossoneri finished eighth in Serie A last season, some 45 points behind champions Juventus, and missed out on Champions League and Europa League football for the coming campaign.
Milan also performed poorly on their recent tour of the United States, with Filippo Inzaghi's men losing all three matches in the International Champions Cup. However, De Sciglio is unconcerned and expects his team to challenge in the league, given the amount of time that they will have to prepare for fixtures without European commitments.
"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 but the full-back revealed the issue is not serious, although he could miss two weeks of training.
He explained: "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."