Marc Lievremont said he felt "immensely sad and immensely proud at the same time" after his reign as France coach came to an end with an 8-7 defeat by New Zealand in the World Cup final.
"People have always said and thought that the All Blacks were the greatest team of all time," he said.
"But tonight I think it's France that was great, and even immense. It's tough to take, we needed a little bit more."
"We did our utmost, and fell short by a point," said captain Thierry Dusautoir.
"Of course we're very sad at the outcome, but we had some luck in the previous match, and that's the way it goes. That's part of sport as well."
The departing Lievremont, who turns 43 on Friday, will be replaced by former Sale boss Philippe Saint-Andre.
He fell out with his players during the tournament and admitted he had experienced a roller coaster ride as boss of Les Bleus.
"I have often spoken about emotional contrasts over the four years I've been in charge, and at this World Cup," he said. "This is the case once again tonight."
France had come in for major criticism after some poor performances on their way to the final.
They lost twice in the pool stages and then struggled past 14-man Wales by a single point in their semi-final and Dusautoir, named man of the match at Eden Park, admitted they had been through "some difficult moments".
"We have been criticised, but today we were strong and we showed that rugby is not just skills... it is also mental," he said, adding with a smile, "although perhaps today we needed more skills".
He continued: "Tonight, everybody was nervous... them and us. There were 30 guys on the pitch and I think they were all scared.
"We rode our luck as best we could but we failed by one point."