A man who represented both clubs in his playing days is among those to have seen the Red Devils adopt a more conservative approach, which sits in stark contrast to the more cavalier philosophies of their arch-rivals at Anfield.
Mourinho has faced criticism for the manner in which he sets about delivering success, with the Portuguese accused of deserting the attacking instincts which made United so devastating during the reign of Sir Alex Ferguson.
Owen believes Mourinho will be given time for as long as he secures silverware, with the Red Devils in no position to demand substance and style after making an appointment designed purely to get them over an alarming slump endured under David Moyes and Louis van Gaal.
"Manchester United are synonymous with the attacking football Sir Alex Ferguson demanded during his 20 years winning trophy after trophy at the club and to ask fans that are used to that and have been brought up on that to accept something different now is difficult," Owen told Yahoo Sport.
"Mourinho has a style that may not be to everyone’s liking and I understand why United fans have expressed concerns about Mourinho’s tactics and that problem will continue, as he is not going to change for anyone.
"Winning has always been more important to Mourinho than how he gets to that destination and United knew that when they hired him, so they are in no position to complain now. Mourinho has a proven method of success and he confirmed that again last season by winning two major trophies.
"What I question is whether the United supporters will put up with this style of football against the top teams long-term because what is hailed by some as a Mourinho tactical masterclass after a 0-0 draw at Liverpool, the fans of the club he is working for now may not see it that way.
"They want to see their side on the front foot, but winning trophies is a very good way of keeping people happy and there are few managers better than Mourinho at doing that."
Owen has, however, suggested that he will continue to prefer watching his former employers on Merseyside over those in Manchester, with Jurgen Klopp’s 'heavy metal' football producing more of a spectacle than that on offer at Old Trafford.
He added: "If I had to choose between the brand of football Klopp promotes and the Mourinho variety, you would have to say that Klopp’s is more entertaining.
"Some of the attacking play Liverpool have produced this season has been fantastic, but they have obviously run into some problems as well."