Mourinho has been openly critical of his star midfielder in recent times, saying that his work rate isn't up to standard.
The United hierarchy are aware of the dispirited mood of numerous club's players, but there is a belief, and a hope, that Mourinho can turn the situation around.
Former Premier League midfielder Craig Burley says Mourinho made the right call taking away his leadership responsibilities.
And while many managers are happy to rotate their squads and bring in fringe players for the League Cup - Lampard played his first choice line-up and was rewarded with a win that can only boost his team's confidence.
According to a source who spoke to The Times: "Jose Mourinho told the players that Paul Pogba will not be the captain because he doesn't represent what a captain is and Manchester United is bigger than anyone".
Barcelona reportedly submitted a bid for Pogba in the summer, but it wasn't a realistic offer - £45m and Yerry Mina and Andre Gomes.
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The manager then walked towards Pogba, and said something again, with the World Cup victor turning to Mourinho once more.
The relationship between Paul Pogba and Jose Mourinho hit the rocks before a ball was even kicked, Sportsmail understands, with the manager furious at the way the Frenchman's £89million transfer was announced.
"The only truth is that I made the decision for him not to be second captain any more but there is no fallout, no problem", Mourinho said on Sky Sports.
"As someone who wants Manchester United to do well, I'm fed up of waking up and seeing these headlines. You have 90 minutes to show a different attitude and I think we have to do better".
The manager had also been angered by Pogba's criticism of his tactics in Saturday's 1-1 draw against Wolves at Old Trafford.
Mourinho gave Pogba the captain's armband at the beginning of the season. The players were superb against Brentford and they deserved the chance to play at Old Trafford.