United secured a deserved win over Pep Guardiola’s side on Saturday at Old Trafford, with the atmosphere described as raucous throughout the contest.
The first half ended goalless, but Bryan Mbeumo broke the deadlock after the interval, before Patrick Dorgu added a second 11 minutes later to seal the result.
Speaking after the match, Rooney said younger United supporters were given “a taste of what it was like under Sir Alex Ferguson”, referencing both the intensity of the performance and the noise generated by the home crowd.
Rooney, who won five Premier League titles with United alongside Carrick, felt there was a noticeable shift in the atmosphere since Carrick took charge.
“I wasn’t at the stadium, I was in the BBC studios, but did you see the difference in the stadium? Even when he [Michael Carrick] walked out before the game and he’s trying to pump the crowd up,” Rooney said on BBC podcast The Wayne Rooney Show.
“I think the fans felt something yesterday. They got a taste of what it was like under Sir Alex Ferguson. Some of the young fans who have been through a terrible time over the last 10, 13 years, really, since Fergie left.
“They haven’t witnessed a team perform that well. I’ve been part of some of those teams as well. I’ve played in some of them.
“They haven’t witnessed a team perform that well, with that energy and that belief in their fighting and being brave with the ball, but also being resilient and tough to play against.
“Them fans felt that yesterday and hopefully that’s a glimpse of what we’ve got coming in the next 16 games.”
Carrick, 44, was appointed interim head coach on Tuesday following the sacking of Ruben Amorim and will remain in the role until the end of the season. Rooney expressed hope that the display against City could be a glimpse of what is to come under Carrick’s leadership.
Mbeumo, a Cameroon international, marked his return from Africa Cup of Nations duty by scoring the opening goal, while Dorgu’s composed finish ensured United claimed local bragging rights.
