The flanker is also now a major doubt for Ireland’s Rugby World Cup campaign in Japan.
Leavy was stretchered off in the 63rd minute having replaced Sean O’Brien only 10 minutes earlier.
“Dan’s had a bad injury. I don’t want to get into too much detail. He’ll be out for a while. We’ll get it assessed and take it from there,” Cullen said of the flanker.
“Been a tough year now but that’s sometimes the nature of our game, it’s a tough one for Dan.”
Leavy had just returned from injury, having taken no part in Ireland’s Six Nations campaign.
Jacob Stockdale’s try-scoring blunder will haunt Ulster and the winger after defending champions Leinster came from behind to win a gruelling all-Irish Heineken Champions Cup quarter-final 21-18 at a packed Aviva Stadium.
The joint-leading try scorer from the pool stages with six, Stockdale crucially lost control of the ball past the try-line early in the second half, and despite Luke Marshall’s subsequent try bringing them level, the Ulstermen fell short thanks to Ross Byrne’s 71st-minute penalty a dominant final 41 phases of possession rugby from the hosts.
Cullen acknowledged that the next couple of weeks will define Leinster’s season
“We’re always having to chase the game from so early. Once Ulster had the lead, they were able to play that pressure game on us.
“We didn’t respond particularly well to it, I didn’t think. But ultimately we got the job done. It’s pleasing on one hand, but frustrating on the other.”
Having highlighted their threats leading into the game, the Wicklow man was not the least bit surprised with Ulster’s performance on the night.
“We talked about all the threats that they have,” said Cullen. “(Stuart) McCloskey in the middle of the field gives them go-forward, good direction.
“We even talked about (Jacob) Stockdale going up the left hand side of the field or chipping the ball over the top when he gathered. It all played out, what we talked about.”
Sign up to our mailing list here and we’ll keep you up to the minute with weekly updates from the world of rugby.