Wolves failed to capitalise on a red card for Catalans' Michael McIlorum at the start of the second half as last season's grand final runners-up came away with the points.
Jordan Crowther was sin-binned in the closing stages as the visitors missed big chances to pile the pressure on Dragons.
England and South Sydney great Burgess said: "I'm really proud of the effort, we probably lost a bit of our discipline in the second half and we didn't handle their red card as well as they did.
"I'm happy with the effort, disappointed with the result. Our defence showed some resolve in the first half and they got us just before the break with some miscommunication around a kick and a breakdown in our system.
"We probably didn't match our intensity in the second half but it's a great marker for round one and something to work with.
"We prepped great, our process was good but we need to tidy things up to help us to get the results, that is our challenge and it has been for a number of years.
"I'm really happy with what I saw, I thought we showed great togetherness and I'm looking forward to next week."
Burgess singled out a try-scoring dream debut for 17-year-old winger Aaron Lindop, adding, "It was an eventful night for his debut and he was up against two of the best wingers in the competition.
"It's a really hostile pace to come, it's a fantastic atmosphere here in the south of France but I thought he took his opportunity well and, while there may be some things he's upset with, he has shown what a brilliant player he's going to be and I really enjoy coaching him."
7°C