Rojo, wearing a £1,150 Dolce & Gabbana tracksuit, had to wait outside Barclays bank while staff were filling up the cash machine.
England left back Shaw, meanwhile, was seen dressed in all black as he went out with his friends.
It has been a frustrating season for Rojo, who has struggled with injuries and has made just three appearances.
Shaw, meanwhile, has featured prominently and played the entirety of the 2-0 defeat to Arsenal at the weekend.
That loss was the first time that United had been beaten in the Premier League under caretaker boss Ole Gunnar Solskjaer.
Solskjaer has won 14 of his 18 games in charge and seems set to be given the United job on a permanent basis.
United are back in action on Saturday when they travel to face Wolves in the quarter-finals of the FA Cup.
Solskjaer’s side are currently in fifth place in the Premier League, two points adrift of fourth-placed Arsenal, while they are through to the quarter-finals of the Champions League.
Speaking after the loss to Arsenal, Solskjaer admitted that United were at their lowest point since he took over.
As reported by BBC Sport, he said: ‘We are disappointed with the result but looking at the performance, you cannot say it was a game we deserved to lose. We created five big chances, hit the woodwork twice.
‘When you see the boys work as hard as they do, the attitude they show in training – today we were lethargic in the first 10-15 minutes, did not have the zip and we did not take the chances. Hopefully we will be ready for Wolves in the FA Cup next week.
‘It has been fantastic so far but today is the the lowest we have been because we lost and missed the chance to put pressure on Spurs.’