The Red Devils will now miss out on Europe's premier club competition next season for the first time since the 1995-96 campaign, and Moyes is keen to ensure that their absence will be a brief one.
"It's part of this club, we want to be in it and we'll do everything we can to get ourselves back in it as quickly as we can," Moyes told Sky Sports News.
"We've already done that and we're doing that behind the scenes just now. We'll try and do everything we possibly can to try and get a team which is capable of winning better than we have done recently."
Today's defeat leaves United seventh in the Premier League table, 13 points off the top four and 23 behind leaders Liverpool.