United have banked on Argentina winger Di Maria – signed for a British transfer record of £59.7 million – to inspire a fresh era of success in Manchester.
Much is also expected of striker Falcao, who has joined on a season-long loan from Monaco, capping the end of a lavish spending spree that saw United part with more than £150m in the transfer window.
Ander Herrera, Luke Shaw, Daley Blind and Marcos Rojo have been brought in together with Di Maria and Falcao, prompting debate over how manager Louis van Gaal can best utilise the players at his disposal.
Van Gaal is confident the new arrivals will help United recover from a poor start to the campaign.
"We bought five players and one player is on loan here and maybe we can buy him next season, and that's Falcao," said the Dutchman.
"We let go [of] 14 players. How to fit in these players is not so difficult, I think, when you let go 14 players and only six players come in.
"They have to perform our philosophy [against QPR] and that philosophy is not so easy to perform. We have seen it already.
"But I think the players we have selected [in the transfer window] shall do that better."
United have still not won this season, with two Premier League draws and a loss to Swansea City having been registered together with a shock 4-0 League Cup loss at MK Dons.
The defeat to Swansea came at Old Trafford and Van Gaal, who is without Phil Jones (hamstring), Marouane Felliani (ankle), Chris Smalling (groin), Michael Carrick (ankle) and Ashley Young (knock) – will be desperate to avoid a repeat.
Van Gaal has faced criticism from certain quarters for letting Danny Welbeck join Arsenal for £16million on transfer deadline day.
Welbeck – a product of the club's famed academy – scored both goals in England's 2-0 win in Switzerland on Monday but Van Gaal claimed he sold the striker because he was not prolific enough.
United will certainly expect goals to flow for the remainder of the campaign, with Wayne Rooney, Robin van Persie and now Falcao available.
QPR sit two places higher than United in the table after a 1-0 win over Sunderland last time out lifted them to 12th.
The Loftus Road outfit are clear underdogs this weekend but boss Harry Redknapp has urged his side to take the game to United.
"Manchester United [have] got a formidable front-line. It will be interesting to see how they gel," Redknapp said.
"They've got a top, top team now. We've got to go up there and make sure we work hard and give them a really good game. We will be ready for it."
Joey Barton could miss out with a hamstring problem but QPR – who are set to start ex-United defender Rio Ferdinand – could hand debuts to new signings Eduardo Vargas and Sandro.
