Despite losing 2-1 to Roma on Thursday, Les Gones managed to progress 5-4 on aggregate after their brilliant 4-2 win in last week's dramatic first leg.
Friday's draw saw them pitted against Turkish champions Besiktas in next month's quarter-finals in which the French club will enter hoping to continue their journey towards a maiden major European trophy.
Genesio admits he is delighted with his side's progress to the last eight but says they cannot get ahead of themselves by prematurely looking beyond their next opponents.
He said: "It's a huge pleasure to take OL into the quarter-finals. We still have the objective of going all the way but there are a lot of good teams left in the competition and we have to stay humble."