Jones demands more despite England's 'perfect' 10
The Australian coach told a post-match media briefing that they were "nowhere near good enough".
Saturday's 37-21 victory over South Africa at Twickenham came just over a year since a World Cup where the tournament hosts failed to get out of the group stage.
That embarrassment led the Rugby Football Union to ditch Stuart Lancaster and bring in former Australia and Japan coach Jones.
The improvement has been significant, with Jones guiding England to a Six Nations Grand Slam and a 3-0 series win in Australia this year.
And on Saturday, in the rain at Twickenham, England ran in four tries as they beat the Springboks for the first time in a decade.
England were sharper than the Springboks, despite a lengthy injury list, but Jones believes even better is to come.
"There's always been depth in England rugby," said Jones.
"I think it's about the players having more ambition.
"One of the most pleasing things for us is to have three of the six nominations [centre Owen Farrell, No.8 Billy Vunipola and lock Maro Itoje] for world player of the year now," added Jones ahead of Sunday's World Rugby awards in London.
"When I took the job I had no expectations," insisted Jones, who has overseen England's rise to second in the world rankings, behind New Zealand.
"All I knew was I was inheriting a very good side that was put together by Stuart Lancaster that had oodles and oodles of talent. My job was to make sure that talent produced performances.
"We're starting to do that, but we've got to get better. We're nowhere near good enough at the moment."
England conceded six penalties in the first 20 minutes before they rallied under captain Dylan Hartley.
"It was good leadership by Dylan, Owen, Billy, they pulled everyone into line," said Jones.
"Basically my job is to make myself redundant. When I'm redundant then the team's going to be functioning well."
England's depth was demonstrated by the performance of their two locks.
Joe Launchbury was named man-of-the-match, while Courtney Lawes marked his 50th Test with a maiden international try.
Neither would have started, however, had the injured first-choice second-row pairing of George Kruis and Itoje been fit.
"Courtney's played his 50th Test and his next 50 is going to be better than his previous 50," said Jones.
"Both of those guys did very well against what was a very good line-out."
England continue their end-of-year programme at home to Fiji on November 19.
But with Argentina arriving at Twickenham the following Saturday, Jones could make changes ahead of England's final Test of 2016 against Australia on December 3.
"We won't just be randomly giving caps to guys who didn't play today [Saturday], I can assure you of that," said Jones.
Agence France-Presse
