When quizzed on where United, who have been heavily linked with Robin van Persie, Lucas Moura and Leighton Baines in recent weeks, are in terms of signing new players, the Scot told reporters: "We are trying to add to the squad and are working on one or two things."
Kagawa, who struck in the 68th minute, was awarded with the sponsors' man-of-the-match award and impressed Sir Alex with his all-action display in his role just off the forward.
On the Japan international, the Red Devils boss enthused: "I thought he was terrific. He was involved in everything, all our interplay, all our possession, he was involved in most of it."
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"Bebe did fantastic to set [Kagawa] up for the goal, I thought he did really well when he came on," the United boss declared.
"I was very pleased, I thought in the second half we did very well," the Scot continued. We upped the tempo of the game and we tried to get more players into the penalty area.
"I thought that in the first half, although we had a lot of possession, I thought we were a bit pedantic and lacked the penetration in our speed of play but the second half we did very well."
The 70-year-old admitted that Shanghai, the team for whom former Chelsea forwards Didier Drogba and Nicolas Anelka now play, had given his side a run for their money.
He continued: "I think it's been a great workout, [the United players] had to really run a lot because [Shanghai] were very organised, as you saw.
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A fellow new signing, Powell, was also given a run-out from the start and was on the end of a rough challenge from Wang Shouting, but Sir Alex was happy with the youngster's showinng.
"Yeah, it was a bad tackle, but he got up and played on," the manager added.
"I thought I'd take him off at half-time with his first introduction to starting a game and he looks a really top player, the boy, he's going to be okay.
"I think that it's always pleasing that the work [that the new signings] do in training transmits itself to an actual match situation, which we saw a lot of tonight so that was good. I'm pleased with that."