United bounced back from losing to Brighton and Tottenham with a comfortable 2-0 victory at Burnley on Sunday to quell some of the mounting tension at Old Trafford.
Mourinho has routinely clashed with the media in recent weeks, demanding more respect for his managerial record, and his superiors at the club over a lack of transfer activity.
However, Schmeichel cited the two trophies won by the Portuguese during his first season in charge in 2016/17 and a second-place finish behind Manchester City last season — United’s highest league finish since Alex Ferguson’s retirement in 2013 — as signs of progress.
“We are progressing, we’ve had a really tough awakening since Sir Alex and (former chief executive) David Gill left at the same time. It left the club without a certain type of experience that the biggest club in the world needs,” said Schmeichel on Monday.
“We’re getting there, we can talk about mistakes but we’ve got Jose Mourinho, a proven winner… he’s won the Europa League, won the League Cup, been in an FA Cup final, we are doing really well and on the way to do doing better.”
Mourinho has been criticised for not getting the best out of star signings Paul Pogba and Alexis Sanchez, and a negative style of play not in keeping with the club’s traditions under Ferguson.
But Schmeichel, who won five Premier League titles during the Scot’s time in charge at Old Trafford, believes there is still enough for the fans to be excited by.
“We’ve got players in the squad that are inspirational, that you want to go to Old Trafford to watch. It all just needs to come together and that takes time.
“I’m like any other United fan. I want us to win everything, but I’m also a realist and I know other clubs have made incredible moves.
“I’m very patient, I know it is going to take time for Manchester United to get back to the level we used to be at, but I’m absolutely convinced that we will get there.”
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