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Aironi announced their arrival in Europe last season with a 28-27 home victory over Biarritz Olympique and McLaughlin is wary of Ulster being the victims of another major giant killing.
"We have got the five points and we are happy with that but we know it is going to be exceptionally tough over there," he said.
"They are more than capable of one big game - and they have already proved that in this competition - so we just have to make sure it doesn't happen against us.
"We know they beat Biarritz Olympique in the Heineken Cup last year and we are under no illusions it will be a tough game.
"Aironi are more than capable of turning us over at home if we aren't on the money, so we know we have to go there and do a job.
"We know this week is a whole new ball game and we are only at half-time and we have to go there and do the same but we know what they are capable of achieving.
"We just have to make sure that when we get the ball we are clinical and play in the right areas of the pitch, if we don't do that they will cause us problems over there.
"In the first half at Ravenhill we played exceptionally well at times but we know we are not the finished article yet.
Meanwhile new signing John Afoa warns he and the rest of the Ulster front five are coming together nicely at just the right time.
"I am building things up," said prop forward Afoa, a World Cup winner with the All Blacks in New Zealand in October. "I had two weeks off so this is only my second game back but you know the combination with Rory (Best) and Tom (Court) and the back five is coming along nicely, which is good.
"Paddy (McAllister) started against Aironi and is a real talent. We put a lot of pressure on him during the week and he had to step up. He did that and we were very happy with how it went - he really delivered and put the pressure on the rest of the pack.
"The match was a little bit scrappy at times but we are happy with the five points. The scrum went OK and the line-out was good but the breakdown is an area we need to address for next week as we have to travel across there to their home turf and try and do it all again.
"We have got a longer week with it being a Saturday game, so we will have a few more days to recover and to train and tweak a few things, but it is going to take another huge effort."
Ulster have played just six matches against Italian opposition - four against Benetton Treviso and the two against Aironi Rugby last season - and have never lost to Azzurri opposition.
"We scored two good tries in the first half and showed a lot of patience and good rugby ability with the ball, but at the same time there were chances we let go," added Afoa.
"However, in the second half, we took our chances and got the bonus point we needed."
