France conceded six tries, five of them being the result of England's offensive kicks that put them under pressure and Parra's words were damning for his team and their management.
"I think that we are capable of doing what the English do, but are we working on this during training? I think we don't work on it enough, even not at all," the 30-year-old said.
"Yet these are very simple things that are today part of high level rugby. We can do this. But do we work on it? No."
France were all the more exposed that coach Jacques Brunel fielded two centres -- Damian Penaud and Gael Fickou -- on the wings and a winger -- Yoann Huget -- at fullback.
The trio were therefore not equipped to deal with England's 47 kicks, despite edging total possession with 53 percent of the ball over the entire match.
"Their kicking game was world class," said fullback Thomas Ramos, who only came on for the second half, where France limited the damage after reaching the interval 30-8 down.
England played in the empty spaces and France had no response for that simple strategy, resulting in their eighth defeat since beating Eddie Jones's side in last year's Six Nations.
While the hosts' kicks were chased by hungry backs, France's were purely defensive and Brunel's side were almost always on the back foot.
"It's hard to find solutions after such a game," Mathieu Bastareaud conceded after France suffered their worst defeat to England since 1911.
"After such a masterclass, we all need to question ourselves. From A to Z," said Parra. "We, the players, try to find solutions but it is complicated."
Lock Sebastien Vahaamahina added: "We have to open our eyes on the areas we need to work on."
With the title already well out of their reach, Les Bleus must now avoid defeat against Scotland at the Stade de France on Feb. 23 if they do not want to play a 'wooden spoon' clash in Rome against Italy in their last outing.
(Reporting by Julien Pretot; Editing by Christian Radnedge)
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