Stephen Ferris continued his RaboDirect PRO12 scoring form with another try while Adam D'Arcy, Andrew Trimble, Paul Marshall and Paddy Jackson also crossed.
Tommaso D'Apice scored Aironi's only try but Ulster will need another maximum point win to keep their European hopes alive in a tough group featuring Leicester and Clermont Auvergne.
McLaughlin said: "We know we can do better and we know we are capable of better. Next week we'll have to do it all again.
"We've got the five points, and we're exceptionally happy with that, but we've got to look at the tries we scored, at the way we moved the ball and we've got to do that time and time and time again next week.
"We took our chances well in the second half and got the bonus point we needed, but next week it's a whole new ball game - it's only half-time. Last year Aironi beat Biarritz at home and they're more than capable of producing a big game."
Elsewhere Dan Parks was the hero for the Cardiff Blues in Pool Two as he kicked his side to a 25-8 win against Edinburgh.
Parks notched 20 points with the boot, including four penalties and two drop-goals, while Alex Cuthbert scored the Welsh outfit's try as Edinburgh could only muster a Lee Jones try and a Greig Laidlaw penalty in response.
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