Carrick unfazed by Rooney support for Man Utd job
Carrick's side stepped up their bid to qualify for next season's Champions League thanks to second-half goals from Casemiro, Matheus Cunha and Benjamin Sesko.
United are in third place in the Premier League, three points ahead of Villa as they chase a top-four finish.
A seventh win in nine games since Carrick took over as interim boss put United six points clear of sixth-placed Chelsea, firmly in the driving seat for a Champions League place.
Rooney said told BBC his former team-mate Carrick should "100 per cent" get the job.
"I know him very well," Rooney said.
"I know his character, his personality. It needed a calm head, but someone who knows the place and the players needed some love, and he has given them that.
"We have seen the players play with more quality, more together as a team, and they look like a very strong team. For me, why would you change?"
Carrick would clearly love to take the job on permanently after a glittering playing career at United.
His only other experience as a manager ended in disappointment at second tier Middlesbrough, but the former England midfielder has proved a steady influence at United after Ruben Amorim's turbulent reign ended in the sack.
United co-owner Jim Ratcliffe this week said Carrick was doing an "excellent" job but stopped short of guaranteeing he would remain in charge after this season.
'It doesn't affect me'
Asked if he was able to ignore the speculation over his future, Carrick said: "There's not that much noise is there? I don't mean Wayne, just in general. It's only noise if you listen to it.
"It doesn't affect me one bit, to be honest. I'm in this position at the moment, doing the best I can, loving it obviously, and we keep pushing for more.
"We want to make the team as good as possible and keep improving. Whatever is going to happen is going to happen."
Bruno Fernandes' pair of assists made him only the third United player in the Premier League era to reach 100 goals and 100 assists, joining Rooney and Ryan Giggs on that landmark.
Fernandes has been key to United's renaissance under Carrick and the Portugal midfielder now has 16 assists this season, chasing down the record of 20 for a single Premier League campaign jointly held by Thierry Henry and Kevin De Bruyne.
"Bruno has done it for a long period of time now," Carrick said. "In the big moments, making a difference whether he's scoring or creating, he's normally around it."
Villa lost a third consecutive league match as their top-four bid splutters, but boss Unai Emery tried to accentuate the positives.
"Overall I feel we did good things but it was not enough," he said. "We need more, but we are progressing.
"After the fantastic months in October, November, December, in the last two months struggling, we are recovering confidence again, working on things in our structure and the players are feeling better.
"Today the result is not changing, we were expecting that could happen because Manchester United here at home now are in a good moment and played very intelligently, but we competed and this is the way I want to keep it."