The visitors clung on to win 20-16 at Murrayfield as the TMO and referee Nic Berry decided not to award a try despite Sam Skinner appearing to ground the ball on the line.
Berry had initially ruled no try on the field and said there was not enough conclusive evidence to overturn that decision.
"We were celebrating in the coaching box having seen the pictures (of the ball) being placed on the try line," said Townsend.
"I don't understand the rationale when you see the pictures and hear the conversation between them (referee and TMO). They have said the ball is placed on the try line."
Scotland had led for most of the match after going in front through Ben White's early try and three Finn Russell penalties.
Gael Fickou's score reduced France's deficit in the first half and they went in front for the first time in the game 10 minutes from time when Thomas Ramos converted a brilliant individual try by Louis Bielle-Biarrey.
Ramos added a penalty to stretch the lead to four points before Scotland appeared to have snatched victory at the death to back up a thrilling 27-26 win over Wales last weekend.
"The emotions were what a fantastic win, what a team to come back, great victory for our supporters and it is taken away from you," added Townsend on what he thought about the late call.
Relief for Galthie
By contrast, the decision brought relief for embattled French coach Fabien Galthie after his side were humbled 38-17 by Ireland last weekend.
Galthie hailed his side's resolve to come from behind after a week of stinging criticism back home for their display against the Irish in Marseille.
"This is a sport of combat, you have to be combative. One has to accept that there are times of adversity," said Galthie, whose side have still only lost to Ireland in their last 12 Six Nations matches.
"We dealt with that this week. We lose together, we suffer together, we win together."
Les Bleus are suffering a hangover from failing to win the World Cup for the first time on home soil last year.
France were again far from their best in a performance littered with handling errors in the wet Edinburgh conditions.
Galthie, though, said a victory was what mattered most to keep their chances of winning the championship alive, should Ireland slip up.
"Given the context, it is OK," added Galthie. "We are not here to give demonstrations of perfect rugby, we are here to win matches."
Both sets of players and fans were left in suspense for more than four minutes as they waited for the officials to decide the fate of the match.
"It is very good for the suspense and audience," said Galthie with more than a hint of sarcasm when asked for his opinion on the decision.
"It is very good to check the television for four minutes. The advertising and the show is up.
"At the end we are happy."
