After a goalless first half, Cameroon forward Mbeumo – returning from Africa Cup of Nations duty – fired United in front, with Dorgu doubling the lead 11 minutes later.
Rooney said it was the “best performance” he had seen from United in a long time.
“I think what Michael has done with the team wasn’t rocket science. It was a simple tweak in terms of what he’d done in terms of formation,” the former England striker said.
“I think everyone’s been talking a lot about Ruben Amorim’s formation in the back three and how it suited Man United as well.
“So he changed that, but if you go back to the last podcast we’d done when I spoke about what United need to do, it’s simple really, it’s run and work hard. It was so refreshing to see the players do that.
“I thought Amad and Dorgu on the wings were excellent, the work-rate they put in to help the full-backs out and they got into a compact shape, which I spoke about, and hit Man City on the break.”
Amorim was dismissed on 5 January and Rooney said United’s win over City was “night and day from what we’ve been seeing” under the Portuguese.
Rooney added: “You can feel it from the fans as well, the difference in energy from the team, the confidence, the belief, the composure on the ball at the right times.
“It was night and day from what we’ve been seeing, so it was such a good day. It reminded me, when we talk about Man United’s DNA, that was it…
“Work hard, run for your team-mate, get back into shape, be hard to play against – [and then] when you get an opportunity run forward.”