Thrilling England win 'starts something' for Galthie's France
Les Bleus fly-half Thomas Ramos kicked the match-winning penalty with 55 seconds of the game remaining in Lyon as they finished second in the Six Nations table.
It came almost five months to the day from October's quarter-final defeat by South Africa in the World Cup in Paris.
"We can do better but at the end of the day we fought, it was hard but the team fought into the final minute," Galthie told France Televisions.
"This team doesn't want to just go away.
"It's not the end of the Six Nations but the start of something," he added.
Galthie's side recovered from a very sluggish start the campaign, including a home humbling by eventual Six Nations champions Ireland.
A victory over Scotland followed before a drab draw at home to Italy.
They were criticised by fans, media and former players as they seemed to suffer a World Cup hangover before last weekend's victory at Wales and the win over England offered some light relief.
"Everything moves so quickly, they are just men, everything is so fragile," Galthie said.
"We’re human beings, not machines.
"You have to be resilient, be coherent, it's important," the former France captain added.
In Lyon, France survived a momentous fightback from England which included three tries in a six-minute blitz either side half-time.
The visitors then led with 60 seconds remaining after an imperious George Ford kicked a touchline conversion following Tommy Freeman's 75th minute try.
"We weren't beaten tonight, we just ran out of time," England head coach Steve Borthwick told reporters.
"The team stayed composed and kept sticking at it, they found the score before half-time.
"Everyone watching that would say we had another score in us."
Borthwick took over in late 2022 and led the side to third place in the World Cup with a conservative playing style.
During the Six Nations Borthwick's side have showed glimpses of attacking brilliance, including not only the four tries against France but also an impressive win over Ireland.
The bonus point against Les Bleus helped England to finish third in the table.
"The team is developing a points scoring ability. As soon as we got into the opposition 20 metres we showed we could score," Borthwick said.
"We have a mix, this is a new team," he added.
