Mourinho has seen his side slip to defeats against Brighton and Tottenham in the first three weeks of the season, but despite reports of trouble behind the scenes, he has been backed by the Old Trafford hero.
Although the 3-0 loss to Spurs was the worst home defeat of the manager's career, Robson, who played 345 times in the league for the Red Devils between 1981 and 1994, says the Portuguese’s track record of success should not be ignored.
“It’s too easy. The minority of fans in clubs will be asking for the manager's head after a few bad results and it’s often they speak the loudest,” he stated to MUTV.
“The track record that Jose has holds up. After three games, you don’t talk about sacking the manager, you encourage and back him.”
Robson, though, was not without criticism. In the wake of Mourinho admitting that he does not know his strongest defence, he instructed the embattled former Real Madrid and Chelsea boss to strengthen his rearguard by sticking to a partnership instead of chopping and changing.
“What I’d like to see is Jose picking two centre halves he trusts and see them for a run of games," he said.
“We need two defenders who know each other properly. Like Rio Ferdinand and Nemanja Vidic and others but the centre halves have also always been in the team. It would be nice to see that for a run of games and get clean sheets.”
Reports have surfaced following the Spurs defeat that Mourinho could be gone by the September international break, should United suffer a third loss in four matches. They travel to Burnley on Sunday on Premier League duty and do so under a weight of negative pressure.
Mourinho took charge of the side in 2016 and enjoyed success in both the EFL Cup and Europa League during his first season in charge. Last term, however, he was unable to separate up any silverware.
Over the course of the summer, he was thwarted in his attempts to strengthen the squad, with the board unable to get a move for a centre-back over the line, despite numerous targets being touted, including Tottenham's Toby Alderweireld and Leicester City's Harry Maguire.
Meanwhile, his relations with players such as Anthony Martial and Paul Pogba are said to be frayed, and after the Spurs loss he stormed out of a press conference after a brief rant.
As such, Robson's viewpoint is not universally echoed, with his former Old Trafford team-mate Paul Parker calling for Mourinho to depart.