But Cockerill admits that European rugby is a different environment and that Leinster will quickly put an end to his side's latest continental quest if they repeat their recent first-half showings at the Aviva Stadium this weekend.
"Leinster are a very good side. If you give Leinster those opportunities, like we did last week against Bath or this week against Quins, we'll be 30 points down at half time. So we've got to be a lot better," said Cockerill, after his men over-turned a 10-0 defict to win 17-13 at The Stoop.
"We didn't play like Champions in the first 40 minutes. We were poor. We've got to play out of our half better and we've got to control the game better at nine and 10. We didn't put into practice what we did on the training field.
"At 10-0, we were probably fortunate not to be further behind. We shouldn't look past that.
"But at half time we regrouped. We said that we'd just keep playing. We needed to play, get some ball, carry it, build some phases and create some opportunities to score. When we do that, we're good.
"When we don't do that and we start to play individually, we end up in a bit of a messy game where we let sides carry at us. Any side being carried at is always going to struggle."
Leicester have won five of their six Premiership games since the end of the Heineken Cup Pool stages, with four of those triumphs coming on the road.
But while most clubs would be delighted with those results alone, Cockerill has made it clear to his players that they will need to step up things up a notch in Dublin.
"We've got to start working better as a collective," added Cockerill.
"We've got really good individuals with good skills there and we just need to channel those skills at the right times and make sure we play in the right areas of the field.
"We put ourselves under pressure by not executing properly against Quins. When you turn the ball over in their 22 four or five times, that hurts you. They don't, they put pressure on you and they get some opportunities to score points. We deal with that - we're realists if nothing else.
"Watching us over the last couple of weeks, I don't know what you'd make of us. Really poor at defending but we take our chances when we get the opportunity, maybe. It's an interesting one."