Ulster coach Mark Anscombe admitted that there had perhaps been an element of luck to scrum-half Ruan Pienaar's score-levelling try and conversion at the end of the third quarter.
But that said, he highlighted the fact that Ulster had identified the hosts' out-of-hand kicking in tight situations as a possible chink in their armour.
"Maybe it was fortunate that we got a charge-down but it was something that we targeted," Anscombe said.
"We wanted to put pressure on their kickers and it's a strength of Roo's that he reads it well.
"The ball was kind to him in staying in-goal."
"Ten points up, we needed to control the game better in the field position and all those things, but we didn't manage that back third as well as we would have liked and they exposed us there," Cockerill said ruefully.
"But to lose to a charged down kick for a try is disappointing, but you you make your own luck.
It's a three-point ball game, they win it on a charge-down from a kick and you can't really account for it.
"Fair play to them for putting us under pressure and they got the result."
But just as Tigers scrum-half Ben Youngs had riled Ulster during the build-up by suggesting "they don't play much rugby", Cockerill too was unable to resist a snide remark regarding the victors' style and their forthcoming quarter-final pairing with Mark McCall-coached Saracens at April.
"That'll be an interesting game plan won't it between the two of them; there won't be much passing, will there?" the former England hooker said. "Ulster are a good side, they played very well. Whether you need to play more rugby to win the tournament is debatable, that's subjective.
"But they're a good side, no doubts about that, and playing at home in the quarter-final is massive for them."
Pointing to Ulster's success in getting the home draw that had been their target since the draw for the six pools was made last summer, Anscombe also underlined the magnitude of the task his players faced on Saturday night at Welford Road.
"We pride ourselves on how we play at Ravenhill and Leicester do that here. They've got a great track record and they're a quality team," he said.
"You know you've got to play 80 minutes and play to the end to do it (win at Welford Road).
"We showed a lot of character to hang in there when we weren't playing perfectly. We showed a lot of resistance and resilience to hang in there and keep our discipline and not allow them to get some penalties," he said.
Captain Johann Muller made no attempt to conceal his delight at Ulster having got what they wanted following their magnificent six out of six in the pool stage.
"That's what we came out here for – to get a home quarter-final," he beamed. "We've got Saracens and they totally outplayed us last year. They're a great side; they don't mind going away from home.
"But it's two months away and I think at this stage that we'll just enjoy this moment."