Injuries no excuse for Scotland
Scotland lost four players to injury during the course of the match at the Stade de France, starting with the captain and first-choice kicker Greig Laidlaw with an ankle problem after just 25 minutes.
Three more players also hobbled off while centre Alex Dunbar was forced off for five minutes after a knock to the head, although he was able to continue.
"We train for these types of scenarios. It's not ideal but we certainly wouldn't use it as an excuse," said New Zealander Cotter, who preferred to focus on his team's at times heroic defending.
"The players showed a lot of courage not to take a try in the last 10 minutes on our line. We defended well."
He added: "Some of our play didn't link well, we'll have to look at it. We lost players but we regrouped pretty well."
Scotland outscored France by two tries from Stuart Hogg and Tim Swinson to one from Gael Fickou but couldn't match their opponents' power at times and gave away a succession of penalties.
French kicker Camille Lopez scored 17 points with the boot while Finn Russell managed only two penalties on his register.
"The game was stop-start at times, we couldn't get a rhythm to our attack," moaned Cotter.
"Our first try was well constructed but at times we lost shape. Credit to the French, they came at us, they were very physical.
"The breakdown was a tough affair. To come away with one point is better than no points."
France captain Guilhem Guirado felt his side would need to improve at the breakdown ahead of their trip to Ireland in two weeks' time.
"It was a scrappy match, there was a lot of disorganised play where we struggled," said the hooker.
"We only had three or four balls maximum to play with. The match was broken up by lots of turnovers.
"The breakdown was crucial because we gave away seven or eight penalties. That showed what we've got to work on before Ireland."
While France coach Guy Noves said the most important thing was the victory following three narrow defeats in a row to Australia, New Zealand and England, he admitted that he wasn't happy with the performance.
"Obviously in terms of the content, we're frustrated. Even though Scotland took their chances with their qualities, they really disrupted us in the rucks," said the former Toulouse boss.
"We spilt quite a few balls and were weak in the scoring zones.
"Maybe the pressure of needing to get a result affected the team but I'm delighted for them.
"We lost in the final 10 minutes against England due to a lack of character, but today that period was in our favour."