The Irish side come up against the Aviva Premiership pace-setters at Ravenhill with a spot in the semi-finals up for grabs.
"We have to be very careful that we play the game, not the occasion," Best is quoted as saying by the Irish Examiner.
"It's going to be a massive, massive game. It's the first quarter-final here since 1999, new ground, splendid stadium, the complete redevelopment to accommodate 18,000 people, so it is going to be a big honour to play here in front of such a crowd.
"It's going to be an emotional occasion. There will be an electric atmosphere and we have been making sure this week that we have everything right, every detail covered so that we can ride over that little bit emotion."
Best, who has 75 caps for Ireland, joined the club in 2004.