Foster said it was 'a heck of an opening game of the World Cup' and congratulated France, who he felt were the better team.
"I was really satisfied with a lot of what we did, but they managed to squeeze us for territory and possession in that last quarter and put pressure on us. It is a certainly a big win for them but it doesn't change a lot. We have just got to find another way through this pool."
Foster said skipper Sam Cane was forced out of the game due to an injury suffered at the captain's run the day before the game.
"He was lifting a jumper at a lineout. He brought them down and felt his back get strained. It was pretty stiff last night, and we had a look at him this morning and decided to pull him. It has freed up, and he is moving better than yesterday, but we didn't have clear information about how bad his back was.
"He says he's had it before but we will check it out properly. His back went into spasm around a disc, but it doesn't look too serious at this stage."
Being the first loss the side has suffered in a World Cup pool game, Foster was unconcerned about the history side of things.
"I don't think we have to rebuild. Stats are stats. I understand all that. But in the past, we have won all our pool games but not the tournament; our goal is to win. This was always going to be massive, and we know how strong France is.
"You saw ambition from us, and whenever we had the opportunity to play, we were pretty efficient at taking it. But they denied us opportunities to attack them in their half. It was frustrating that some of the pictures we painted for the ref at the scrum were penalised, and perhaps they were painting slightly different pictures and getting away with it.
"There were some good lessons for us. We fired some good bullets, we just didn't fire enough.
"The ball's bounce for France's second try had inflated the scoreboard difference between the sides. He felt the All Blacks missed a chance to deal to France in the final moments of the first half.
"I thought they were out on their feet in the last 10 minutes before half-time and we should have been a bit more efficient. We missed it in the corner with a loose pass, we weren't quite good enough."
The penalties conceded were the result of French pressure.
"You have to give France some credit for that. Will [Jordan] was a bit clumsy with a couple of aerial things, and the second one didn't help us. The yellow card came at a bad time against a team who like to exploit the back-field. France were good enough to take advantage of that, but our discipline was pretty good in the first half. When we had the ball, we played with a lot of ambition. There was a lot of good stuff. It was frustrating that we couldn't strike in that second half.
"Most of the penalties were about them getting on the ball really quickly and us not being able to move them. That's something we can control and take lot of pride in. But they have set a pretty high bar for us, so we have been given that message."