The Red Devils look to be well on their way to the final at Wembley on May 28 after cruising to success in Gelsenkirchen as Schalke froze badly in their biggest game of the season.
United would hold a more commanding lead had it not been for an outstanding performance from Manuel Neuer, with the Germany international thwarting everything the visitors threw at him in a one-sided first half.
The pattern of play continued after the interval and the deadlock was only broken in the 67th minute when Rooney played in Giggs, before the England international added a second just two minutes later from Javier Hernandez's pass.
But having seen Ralf Rangnick's men score five away from home against holders Inter Milan in the last round, United star striker insists they cannot afford to relax in the second leg at Old Trafford next week.
"Schalke are a good team and we can't take them lightly. We need to make sure we are professional and fully concentrated," he told Sky Sports.
Giggs insisted the players were confident they would be able to find a goal despite being constantly thwarted by the impressive Neuer.
"We knew that if we kept creating chances one would go in and hopefully I would get one on my left foot rather than my right," he said.
"Before the game we would have taken 2-0 but now we are slightly disappointed."
The Welshman, who becomes the oldest player to score in the history of the Champions League, praised the depth of Sir Alex Ferguson's squad ahead of their weekend meeting with Arsenal.
"We've got a tough game coming up Sunday so the manager rotated and we are obviously pleased, the lads who came on did well too so it's not just about the 11 players, it's about the squad," he said.