De Gea picked up a hamstring complaint against Arsenal last weekend which eventually forced him off.
Meanwhile, Falcao sustained an injury in Man United’s final training session before the Hull clash.
Van Gaal stated that the 29-year-old should make a swift recovery as his injury is “not a big problem.”
LVG said both Falcao and De Gea are injured. On Falcao "it was in the last training session. It is not a big problem."
— Simon Stone (@sistoney67) May 24, 2015
Both players will have been disappointed to miss United’s final fixture of the campaign as it looks increasingly likely that they will leave the club in the summer.
Numerous reports on Sunday afternoon suggested Falcao has been told he has no future at United, while De Gea continues to be strongly linked with a move to Real Madrid.
The hope for supporters is that their situations are cleared up quickly so United can move on ahead of an assault on the Premier League title next season.