Dejected Scott Johnson insisted the better team lost after Jean-Marc Doussain's last-minute penalty gave France victory in the interim head coach's last match in charge of Scotland at Murrayfield.
"That's where the scoreboard lies; we were the better team," said the Australian, who will become director of rugby when Vern Cotter takes over.
"It was one where as a coach you are bitterly disappointed for the boys.
"Sometimes it doesn't add up."
For Scotland, the conclusion of the contest was in sharp contrast to that of their previous Six Nations encounter, a last-gasp win over Italy in Rome.
Man-of-the-match David Denton told BBC Sport the result was "one of the most disappointing things I've had in a Scotland jersey".
The Edinburgh forward said: "We went out there and gave absolutely everything we had and I think we were very unlucky at the end.
"The support for the Six Nations [from fans] has been absolutely incredible. We played really well and we were very close.
"I'm hugely proud of the boys. The front row in particular did very well. This was a French team that came here to try and beat us up and take us on at the set piece and I think it's an area we dominated."
The Scots had moved into a 14-9 lead at half-time thanks to tries from full-back Stuart Hogg and Tommy Seymour, the latter a well-worked move that allowed the Glasgow wing to pierce the French back line.
But, as Scotland looked to strengthen their position, Yoann Huget intercepted a pass by Duncan Weir and ran the length of the pitch to level the score and Maxime Machenaud added the conversion to make it 16-14.
A Greig Laidlaw penalty fell short of the posts before Weir put the home side in front with a confident kick that appeared likely to earn Scotland's second victory in the competition this year.
However Doussain's last-ditch penalty, which keeps the French in with a shout of the Six Nations title, left the Scots ashen-faced at the final whistle.
"It's a game we should have won," added Johnson, who will lead Scotland for the last time against Wales next week.
"We played the better rugby, the scoreboard told a different story.
"Once again there's great character in the team. They didn't pack it in. They showed great resolve.
"We showed today we've got quality players. We played really good rugby for a long period. That is the rugby that we need to play."
Johnson was riled by New Zealand referee Chris Pollock's penalty calls, describing himself as "shattered" by the 11-2 count in France's favour after an hour of play.
"You can't tell me in an even contest there is that much disparity between two teams," he said.
"You can't tell me that. I won't have it! I've given up seeking clarity [from the referee]. I can't get my breath back, I'd rather talk about something else."