The Irish side kicked off their European campaign in dramatic style with a 27-26 victory over Sale, Ian Keatley sending over a last-minute drop goal.
And with Munster currently lying in fourth place in the GUINNESS PRO12 table Conway wants to see more "special days" this term.
"It was one of those special Munster days but for me a first," Conway told the Irish Examiner. "It just shows how experienced the lads are.
"We were struggling in the first half, a good few points behind going into that second half and it was invaluable to have those lads who have been through those big European days.
"Keats coming in at the end (with the drop goal) was exceptional; it was the best feeling I have ever had on a rugby pitch.
"It was brilliant to be involved in a day like that. The lads in there who have been involved in days like that before say it was special.
"One of the questions before pointed out that we couldn't afford to start off like we did last year against Edinburgh, losing with the group that we have.
"We have Sarries next week, they are so strong. It was great to be involved in the start of the European Cup and to be involved in a win like that was brilliant."
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