The Red Devils were knocked out in the round of 16 last season and have not made it past the quarter-finals of the competition since 2010-11 - the year De Gea joined the club.
United will begin their campaign on the artificial pitch of Swiss side Young Boys on Wednesday night, and De Gea is expecting a difficult start to the group stages.
"Of course we want to improve in the Champions League. It's such a special competition. It's a long time for Manchester United not to win this cup so we are ready to do it," the Spaniard told reporters.
"We are in a difficult group, starting tomorrow with a difficult team. We want to start well, winning games and try to win the competition but we know it's always difficult to win.
"We are not used to playing on artificial grass so it's going to be a bit different and probably more difficult for us. But we have to train today to see how the balls work on this pitch and try to play our football here. We know it's going to be a tough game."
United have also been drawn in a group alongside Juventus and Valencia in Group H of the Champions League.