United put Giggs in temporary charge of the team on Tuesday following the sacking of David Moyes, who was dismissed just 10 months into his six-year contract.
After the match Rooney backed his team-mate to have a great future in management, strongly indicating that he thinks Giggs is ready to lead Manchester United on a permanent basis.
"Giggsy has got all the credentials to be the next boss but that decision is down to the board," Rooney said.
"He's a really experienced player and he's built to be a manager. We can see that as players, we can see how he's handled himself since he took over."
Reports from Holland claiming that Louis van Gaal has already agreed to take the job suggest that Giggs is not be under consideration for the post on a full-time basis, but many of the 75,208 fans who were inside Old Trafford wish he was.
"To win 4-0 is a dream day for us. It's always nice to end the game like we did," the interim manager said after registering the team's biggest home win of the season.
United struggled to get going in the first half, but after Rooney's penalty - which came after Steven Whittaker pulled Danny Welbeck back - the Red Devils kicked into gear.
Rooney curled a peach of a shot home from 25-yards after the break and Mata scored twice from close range to make it 4-0.
What happened on the pitch was something of a sideshow for most of the game.
The fans had come to see Giggs - the man who is responsible for trying to consign the Moyes era to history as quick as possible.
The fans made their feelings known towards their most decorated player from the start.
Giggs, and his popular coaching staff of Paul Scholes, Nicky Butt and Phil Neville, received a rousing reception as they left the tunnel and throughout the match he was hailed by the home fans.
"The reception was great," said Giggs, who has played 962 times for United. "I've walked down that tunnel so many times in big games and that was the best feeling I've had.
"I felt 10 foot tall, so proud. The fans' reaction was great, just like it has been all week."
It was not all joy for Giggs though.
The Welshman revealed he had tossed and turned in his bed on the eve of the match, worrying about selection dilemmas.
Giggs made an attempt to make a clean break from the Moyes era by making six changes from the Scot's final game in charge - a miserable 2-0 defeat at Everton.
Marouane Fellaini - a £27.5million Moyes purchase - did not make the squad while club-record signing Mata only came off the bench after an hour.
When asked whether he slept on Friday night, Giggs was candid in his response.
"No," he said. "Leaving out players was the reason I didn't sleep. They are team-mates of mine and I've never done it before.
"It was a tough one to leave Juan out. But he put on a half-hour master class. He was brilliant and I was really happy for him.
"It's not easy, he's got a big price tag and to not start the game was disappointing for him.
"I'll continue not enjoying (leaving players out); that has been the hardest part this week."
Giggs will have to get used to that aspect of the game over the next fortnight, and possibly beyond.
Giggs said he would not allow himself to think about the possibility of becoming full-time United boss until the end of the season.
United are after a more experienced manager - even though they distanced themselves from reports on Saturday morning in the Dutch press that they had given the job to Holland coach Louis van Gaal.
The win leaves United six points short of sixth-place Tottenham, who have played one more game.
Norwich can only dream of being in such a lofty position. The Canaries are just one point above the drop zone.
Cardiff and Sunderland both have the chance of plunging Neil Adams' men into the bottom three when they meet on Sunday.
"It's difficult and we will be looking at the results tomorrow," he said. "What we have to make sure we do is give everything we've got.
"We are going to need to take points in each of the games.
"We need to have a real good go at it and need to be a little bit braver than we were today.
"We are still out of the bottom three but we can't rely on other teams, we have to get our own points."
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- Wayne Rooney
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