Instead, Guy Noves' star-studded squad started with a bang as they had the bonus point sewn just past half an hour in racing into a 24-0 interval lead.
"We gave our full respect to Zebre," said Galan, who was preferred to French Test star Louis Picamoles at No8.
"Getting a try-scoring bonus point that quick doesn't happen that often but we managed to achieve that because we did things in the right order - that's why we scored very quickly.
"But the game definitely wasn't as straightforward as it might have seemed - far from it.
"We were rigourous and that's what has to be expected of you during these high-level Heineken Cup games. And we kept being rigourous all match long.
"We learnt from our past mistakes. Last year, those missed points and the opportunities we forgot to take cost us our qualification for the quarter finals."
Next up for Toulouse is an entirely different challenge as they travel to London to face last season's beaten semi finalists Saracens at Wembley Stadium.
And Gallan knows the four-times European Champions will have to be at their very best if they are to return across the Channel with what could be a decisive pool victory.
"We will have to be just as rigourous in Round Two. We will have to show Saracens that we can be just as good against them," added Gallan.
"This is a very big challenge awaiting us in what will be a hostile venue. We know we will have to improve our performance and show even greater application.
"The squad is reacting well together as a group right now. We found some cohesion and I think we showed that on Friday. But we know we have to get better and better, starting in our next game."