Last season may have been United's highest finish since Sir Alex Ferguson retired but the 19-point gap to runaway Premier League champions Manchester City underlined the improvements required.
The Daily Mail says he kept his cool in front of the media ahead of Friday's Premier League opener against Leicester, but privately he was said to be angry and frustrated.
It will be the eighth time the midfielder has captained United and is a big vote of confidence in a player who has made it clear he wants to leave, and Pogba could keep the captaincy when Antonio Valencia returns from injury.
But Mourinho has called on his team to avoid an early slip-up against Leicester and ensure they do not fall behind their title rivals.
"It is hard for me to understand, we finish second which I keep saying, that I won eight championships and three Premier Leagues but I keep feeling the second last season was one of my biggest achievements in the game".
"You try to make a case and there is no case on it". Bayern Munich defender Jerome Boateng is Mourinho's first choice, but has reportedly phoned the Portuguese coach to tell him he won't be joining.
Jose is now forced to somehow challenge for the title with nearly the same squad as last season while his rivals have all strengthened considerably. For example, Alexis Sanchez had a good pre-season with lots of matches and lots of minutes. He didn't have nine days of pre-season where no training, no football, absolutely nothing.
"I said that during preseason and it looked like I was saying something absolutely out of order, something insane, I repeat: Preseason is hard when you don't have your players to work, that's as simple as that".
Mourinho's relationship with players like Pogba and Martial has come under close scrutiny, as have the manager's mood swings over the club's failure to complete key signings he wanted in the transfer window.
But Mourinho, entering his third season in charge at Old Trafford, claimed, in typically confrontational fashion, that there are no problems in his squad or in his commitment to the club.
"I have my players and I like my players, I like to work with my players", said Mourinho. "It is a lie, repeated 1,000 times". Unlike the majority of the United side, Sanchez enjoyed a full preseason and will be raring to go.