But while that form is a clear confidence boost ahead of their trip to Ireland, director of rugby Mark McCall insists they have to be ready to face a side who will raise their game for continental competition.
"We've got a tough first up fixture against Connacht in Galway. And it's not just me saying how difficult that will be: they've beaten Biarritz and Harlequins there and if that doesn't concentrate the mind, nothing will," said McCall.
"They've got a really good product there now. They've got 6 or 7,000 people who turn up and they're close to the pitch and there's a great atmosphere.
"And the Irish teams step it up for this competition, they really do. Connacht fought very hard to get into the competition for years and years and they step it up in particular. For them, this is the be all and end all, especially that first fixture. They'll be stepping up and we've got to make sure we're ready for that."
Saracens have performed impressively at Europe's top table in the past two seasons, reaching the last eight in 2012 and then the final four last time out.
McCall acknowledges that progress has been made at home and abroad but he claims there is no danger whatsoever of his side getting ahead of themselves prior to the Pool 3 opener at The Sportsground.
"The last two years have been good for us with the quarter-finals two years ago and the semi-finals last year. But you don't really look too far ahead in this competition. It's pretty cruel and you can be out of it very quickly if you don't get things right," added the former Ulster and Ireland centre.
"It will be a heck of a challenge in Galway, but we'll look forward to it because our players enjoy playing in those kind of atmospheres. We've got a good togetherness and tightness in the group at the moment and everyone's working really hard.
"Our results over the last couple of years away from home would suggest that our players are pretty good at concentrating - it doesn't really matter where we play, we'll just roll up our sleeves and get stuck in."