The Scots were left chasing a result against France in their fourth and final World Cup warm-up match after wing Noa Nakaitaci's late touchdown put Les Bleus ahead.
But skipper Greig Laidlaw and his players opted against knocking over a simple kick which would have tied the match as they instead chose to go for the win.
The gamble didn't work out as the hosts held out for a 19-16 win at the Stade de France, denying Scotland their first win in Paris since 1999.
Cotter said: "The boys wanted to get the win. It's been a few years since we had one [in Paris]. They wanted to get over the line and created several line-breaks.
"It was a good attitude to take. It was a game where we were testing ourselves.
"It's the players' decision and I completely back it.
"If it had been a Six Nations match of course we would have kicked it but we are preparing for a World Cup and I admire the decision to try to win the game."
Laidlaw added: "If we had kicked the goal we'd have taken a draw but just with the manner of the game, we came to win. It was a team decision in the end and we felt we could win."
Scotland claimed a 9-6 half-time lead and looked set for victory themselves when a moment of magic from Laidlaw put them 16-12 up with 15 minutes left.
The scrum-half fired the ball into a gaping hole in the French defence for Tommy Seymour to score.
However, the joy did not last as Nakaitaci battered through the Scots' defence for the winning try.