Meanwhile, sources also confirmed earlier reports that Chelsea are willing to swap Willian for Anthony Martial, who did not travel to Germany for the friendly with Bayern Munich on Sunday.
"The players were, once more, brilliant, they could not have done better than what they did", added Mourinho to MUTV.
The strained relationship between the two key figures at Old Trafford is the worst-possible preparation for the new season as United look to close the gap on champions Manchester City and keep up with their other rivals.
The comments from Mourinho that have been doing the rounds recently reflect more on how unhappy he is with his own situation in the transfer market than he is with the way Liverpool are spending their money. "I know that he tries the best for me".
"If we don't make our team better it will be a hard season for us".
The latter is now poised to join Everton instead, and the Red Devils have turned their attention to World Cup victor Boateng.
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Sarri also confirmed he would speak to Willian about a passport issue which has reportedly delayed his return. Chelsea manager Maurizio Sarri has expressed his annoyance at Willian's late return to pre-season training.
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"In the week, we have to organise the week in a way so we can be fresh for Friday because, on Friday, the Premier League starts".
Mourinho, who has been linked with moves for Tottenham defender Toby Alderweireld and Leicester centre-back Harry Maguire before Thursday's transfer window, selected Alexis Sanchez as captain in Bavaria.
The final stages proved to be a similar affair for Mourinho's men, as they made no attempt at goal as Bayern held on for the win.
The debacle has shades of the Ivan Perisic chase of last summer; where Jose Mourinho clearly wanted the Croatian, but Ed Woodward did not wish to bid the extra few million to convince Inter Milan to sell.
"Of course, he respected Rooney and then Zlatan wanted to have it. It's something fantastic for the kid, let's give the shirt to him".