With winger Jonny May scoring a hat-trick inside just 29 minutes, the Red Rose inflicted an emphatic 44-8 defeat on the hapless French to continue their excellent start to this season’s Six Nations.
England were keen to build on the brilliant opening victory over holders Ireland in Dublin and they did just that with another dominant display at Twickenham.
However, having led 30-8 at half-time Jones realised they could have been more ruthless.
“When you put yourself in a position where, after 30 minutes, you’ve got a bonus point against a top team you’ve done pretty well,” he said.
“And the second half I thought our performance was even better.
“Even though we didn’t score as many points, our focus and our discipline to keep France scoreless was outstanding.
“But we just had a quick chat in the room there and we felt we probably left 15 to 20 points on the field.
“There’s a lot more in this team and we understand that and we’re committed to being the very best we can be.
“It wasn’t the perfect game, but it also says to us how much more we have in us and that’s exciting.
“When we get back together on Wednesday we’ll start the process of how we can get better again.”
The next test is, of course, Wales in Cardiff on Saturday week.
Warren Gatland’s side also have a 100 per cent record so far following wins in Paris and Rome and they are the only other side who can complete a Grand Slam.
Jones could not resist immediately starting the mind games last night with his barbed reference.
“All I know is that we are playing against the greatest Welsh side ever,” he said. “So that is enough for me.
“(Why are they the greatest?) I hear all the commentary and that is what everyone is saying.
“So how can I argue with the commentary?
“Any time England plays Wales it is a special match, isn’t it?
“Because of the history of the two countries and the history of rugby between the two countries – it’s special.
“You have a Welsh team that is doing so well. If I remember the comments back in November we weren’t doing so well and the gap between us was massive.
“So let’s see how big the gap is a week Saturday.”
Undoubtedly this England team have certainly rediscovered their quality after the travails of last year.
They finished fifth in that Six Nations, their worst Championship placement since 1987, and went on a five-match losing run heading into the summer.
But having worked their way back into form during the autumn Jones’s side look commanding once more with their kicking game especially proving world class yesterday.
Fly-half Owen Farrell, in particular, delivered a master class exposing space behind the French defensive line time after time.
“Yes, it was pretty good, pretty useful,” conceded Jones.
“Owen’s got a good sense of the game, but your kicks are only as good as your chases.
“Some of the chasing was outstanding.
“Jonny May’s like when you got to the park and you see someone with a tennis ball; they throw it, the dog runs 100 miles per hour, chases it and brings it back. He does that pretty well.
“Jonny works unbelievably hard at his game and his development as a winger has come through his own hard work.
“He works very hard on being quick and very hard at being repeatedly quick.”
The Leicester Tigers winger has now scored 12 tries in his last dozen Tests and with 22 in total has moved up to seventh in his country’s list of all-time highest try scorers.
May, 28, said: “I think one day I will look back and be really proud of what I have done.
“But I have not got the time to do that at the moment. We have got a big game coming up.
“I just have to keep working hard.”
Meanwhile, Jones hopes to have lock Maro Itoje fit for Cardiff, but is less sure about co-captain Dylan Hartley being ready in time.