Daley Blind with a knee injury became the third United player to be crocked during the international break.
Manchester United midfielder Marouane Fellaini believes he was made the scapegoat for the team's torrid time under former manager David Moyes in the Premier League last season.
Moyes has agreed to take over as head coach of Real Sociedad until 30 June 2016, the La Liga club announced in a statement on Monday.
United recorded a victory for the first time in four attempts, but they made hard work of their 1-0 triumph against a spirited but limited Crystal Palace on Saturday.
Van Gaal has warned Falcao could face a lengthy absence from his top-heavy side as they struggle to find a winning formula.
Liverpool are at seventh place - 12 points behind Chelsea - and showing none of the form that took the team to a second-place finish last season.
United manager Louis van Gaal says Rojo will be out for six weeks after dislocating his shoulder in the 1-0 defeat to Manchester City last Sunday.
A dismal start to the season and a seemingly never-ending defensive injury crisis have left Van Gaal feeling "lousy".
In what was ultimately a mediocre, error-strewn Manchester derby, we did get to understand much and more about the two teams on the field.
Van Gaal took charge at Old Trafford after leading the Netherlands to the semi-finals of this year's World Cup.
Manchester United's defensive woes have deepened with Rojo's dislocated shoulder and Smalling's red card during Manchester derby.