United missed out on a place in any European competition due to a disappointing campaign last season but a 2-1 victory over rivals Liverpool last time out hugely enhanced their hopes of a top-four finish.
Louis van Gaal's team lie fourth - five points above Liverpool - with eight games to play and Spain international De Gea believes missing out on a return to the elite is not an option United can entertain.
"We have to qualify for the Champions League no matter what," he told FIFA.com.
"We already missed out last season, and a team like Manchester United cannot do that two years in a row."
Villa have concerns of a different kind after a 1-0 defeat to Swansea City in their last outing left them perched three points above the relegation zone.
Tim Sherwood had overseen a run of three consecutive wins in all competitions before that and Villa's recently appointed manager is primed for a pivotal week, when his club hosts second-bottom QPR on Tuesday.
"It is a massive week," he told a pre-match news conference. "We hope we can get a few bodies back on the pitch to give us a bit more impetus.
"Man United is the only game I'm focusing on. We need to get something out of that game.
"It's a wonderful place to go and play. There are a few in our dressing room who have gone there and won and the boys are confident we can do it again."
Sherwood could welcome back captain Ron Vlaar from a calf problem at Old Trafford, while fellow defender Jores Okore is set to return following a knee injury - both welcome boosts in the battle against the drop.
"It was obviously going to be a difficult task," Sherwood said. "Nobody said it was going to be easy. There will be lots of ups and downs along the way but I'm confident we can do it.
"It's a great club, I feel very pleased to have got the opportunity to manage this great club. It is a dream job for me if we stay in the league, it gives me a pre-season to build my own squad. I couldn't have hand picked a better job, but we need to get over the line."
Chris Smalling is expected to be passed fit for United despite being substituted when playing for England during midweek. Van Gaal will assess Robin van Persie (ankle) and Luke Shaw (hamstring), while Jonny Evans remains suspended.
