The Welsh region had been tipped for a resounding win over the French club - but in the end they had to settle for a rather closer encounter, with Bourgoin registering a losing bonus point.
"We are always satisfied to win a game of rugby, but obviously we didn't manage the game as tactically as we would have liked," said Jones.
"But full credit to Bourgoin - they caused us a lot of problems. They 'fronted up' and were superior in their kicking strategy.
"Having said that, we expected a tough game - because they are not third in the French Championship for no reason. They have turned up in the Heineken Cup this year, and that can only be good for the competition."
Ospreys had to work hard for their superiority, and Jones admitted: "They caused us a lot of problems, but there are plenty of 'positives' for us to take out of the game.
"We a have a lot of young kids who need to understand what European rugby is all about. We racked up 98 points and 14 tries in our last two games - but this is a different competition.
"The Heineken Cup has a knife-edge to it, and you have to learn how to control games and make sure you don't slip up."
Jones knows the Ospreys must be sharper when they travel to Kingsholm next Friday to face a Gloucester side who earned a bonus-point victory in Ulster on Saturday.
"We need to pick our game up five to 10 per cent," he said.
"What we saw tonight (Saturday) was a hangover from the EDF (Energy Cup). We knew it was coming. We felt it all week - we thought we could turn up here and throw the ball from side to side. We have learnt a lot of harsh lessons.
"We will have to improve tactically - and when teams kick to us we have to deal with the kicking game more effectively."
Bourgoin lock Chris Wyatt is confident his team have more to offer in the tournament than in previous years.
"Both sides have to improve. We missed chances which you can't afford to do - as did the Ospreys," he said.
"We didn't win - but we were pleased to come away with a point. Perhaps the Ospreys under-estimated us."