Mourinho, who has concerns over the fitness of several players and revealed that Nemanja Matic has had surgery and will miss the start of the season, gave a debut to new Brazilian signing Fred.
The Liverpool squad flew home immediately after the United game and will start a pre-season training camp in France from Monday.
Liverpool made it 3-1 after 72 minutes after Ander Herrera fouled Andy Robertson and Sheyi Ojo converted the penalty. I think today it was a game where it was quite easy to come in for pretty much all of them because we played over 90 minutes of really good football on a very hard pitch for both teams. It happened last year and the year before but now we want to make the next step. His condition was not good when he was back.
Former Stoke City winger Shaqiri didn't just score the goal of the game - a magnificent overhead kick in the second half - but he contributed so much in the final third.
"They arrived here and it was soccer and they had to be in a soccer game".
Fans were out in force at Michigan Stadium, with over 100,000 packed inside the big venue.
As such Mourinho, who still remains hopeful of adding two new faces to his squad before the transfer window closes on August 9, feels the Chile international's disappointment on the pitch is understandable. That's not normal after four days in the club - adapting that well to the style of play. "They will not be here", Mourinho said.
"The only real story I know from MI is the Fab Five", Klopp said.
"I would like to have two more players, I think I am not going to have two", he said. I think I am not going to have two. We played over 90 minutes of really good football on a very hard pitch for both teams.