"They showed no enthusiasm to play the game but we did a good job," Rooney told Sky Sports 2. "As soon as get the first you know they must try a bit to come out and play.
"At times we played some good football but we're delighted with 4-0.
"A few young lads came in tonight and it will give them good experience."
Rooney claimed the performance was testament to United's soaring self-belief.
"We are really confident at the moment anyway," he added. "We've played great football over the last few months and need to keep it going to stay at the top of the (Premier) league."
United boss Sir Alex Ferguson was pleased that a team including several youngsters was able to cope with the challenge put before them by the Ukrainians.
"It was a perfect result and gets us into the next stage so we must be very pleased with that," he told Sky Sports 2.
"They adopted a man-marking system and made it very difficult - it was something new for the young players.
"We got a break with the first goal and it opened up the game up for us."
Ferguson insisted that he hoped the inclusion of rookies such as Pique, Danny Simpson and Jonny Evans would persuade them to stay at Old Trafford in the face of interest from elsewhere.
"It shows they have a great chance at this club so they know their future's here," he added.