Following the sacking of David Moyes earlier in the week, Giggs has taken charge of first-team affairs at Old Trafford and he guided United to a resounding 4-0 win at home to Norwich City in his first game.
A Rooney penalty separated the sides at half-time and he added a second just after the break before Juan Mata stepped off the bench to grab a brace as Giggs' men cruised to victory.
Ahead of the game, United moved to deny reports that Holland boss Louis van Gaal is set to become their new boss after the summer's World Cup.
Giggs will remain in charge for the remaining three games of the campaign, but Rooney believes that he has the ability to do the job on a permanent basis.
"It's strange, I've played with him for the last 10 years. Giggsy's come in and we all know Giggsy is a really experienced player," he told Sky Sports.
"He's been part of the coaching staff for the season. He's built to be a manager, as a team we can see that.
"We can see that by how he's handled himself since he took over so it was fantastic to go out there and get the win for him."
Asked if he would like Giggs to get the job, Rooney replied: "That's down to the board, obviously. I think Giggsy has got all of the credentials to be a manager but that's down to the board."
The win over Norwich saw United have more attempts on goal than they had in any other Premier League game this season, but Rooney believes that was not because of the managerial change.
"I think it's down to us as a team and us as players. We've had a tough week, we understand there's been a lot of negativity towards us as a team and we're hurt by that. We want to put it right," he said.
"We know we're better than what we've showed and today we showed that. It's important for us now to end the season well, and that's what we're aiming to do.
"We knew it was going to be a tough game because Norwich are fighting for survival, and going in at half-time was good for us getting that goal.
"We knew we had to score again and once we did, we broke them down a lot more easy with the pace and thankfully with the four goals it was a comfortable win."
Asked if the players should take responsibility for the poor form under Moyes, Rooney said: "Of course we should. We're the ones that go out onto the pitch and we under-performed.
"We have to take on the responsibility, but we move on. It's a great football club and we have to go and show we're a top team and that's what we plan to do."
Meanwhile, Mata admitted his relief at securing the three points after some frustrating times at Old Trafford this season.
"I have to say that we always try our best. Sometimes it's difficult to win and sometimes it's difficult to play. In the first half it was difficult," he said.
"Norwich came to defend and look for the counter attack and we didn't find enough space to create opportunities. But as Wazza said, we are all together in the good and the bad moments. Now our aim is to win the remaining games."
Speaking of Giggs, Mata added: "For me, it's a pleasure to play under this manager. When I was a kid I remember him playing. He is a proper Man United boy.
"It's a pleasure to be with him in the training ground and at the game, but it's not down to us."