The Red Devils fought back from a two-goal first-leg deficit to beat the Greek champions 3-0 at Old Trafford, with a hat-trick from Robin van Persie sending United through to the last eight.
Rooney played a vital role in the victory that has helped ease the pressure on manager David Moyes and the England international believes that the Premier League champions owed their manager a performance.
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When asked what was the key to victory, Rooney added: "Just desire to win. The fans were fantastic against Liverpool and again tonight they were brilliant and they deserve this. It was a big result, a big performance and we're delighted for them."
United now join Barcelona, Atletico Madrid, Paris Saint-Germain, Chelsea, Real Madrid, Dortmund and Bayern Munich in the draw for the quarter-finals, which takes place on March 21, with the first legs to be played on April 1 and 2.