Louis van Gaal's men crashed out of European club football's elite competition at the group stage, as they finished third in a group also featuring Wolfsburg, PSV Eindhoven and CSKA Moscow.
De Gea is ready to move on swiftly, however, and insists he is keen to win the secondary European competition.
"The Europa League is an enjoyable competition to play in. Naturally I have great memories of when I won in the final [with Atletico Madrid in 2010]," De Gea told United's official website.
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"But this is Manchester United and while we've been knocked out of the Champions League, we are now in another competition and we will be trying to win it in just the same way.
"It's a long competition and a bit different to what we are used to playing in, with the games on a Thursday instead of a Tuesday or a Wednesday, and that can change your regime a little bit. But I think we are prepared and we will be having a real go at winning it."
United meet Midtjylland in the round of 32 and De Gea expects a tough tie against the team that eliminated Southampton earlier this season.
"We've got a tricky tie, but then any opponent at this stage of this competition is going to be a difficult one," he added.
"Obviously, we want to win both legs and hopefully that's what we'll do."