Jones has told Gustard, credited with turning Premiership champions Saracens into one of the best defensive teams in Europe, that he "has got to get better" despite England's perfect record since the Australian took charge last year.
"I worked with Eddie before and knew he would be frank. I don't mind that. I don't want to be an ordinary coach, I want to be the best coach I can be," Gustard told British media.
England won this year's Six Nations before travelling to Australia and beating the Wallabies 3-0. They conceded 10 tries in the series, however, and Jones demanded defensive improvement.
"It's not unfair criticism, it's a critique," Gustard said.
"If you take it personally, then it's your ego and the game isn't about us, it's not about our ego, it's about the players."
Gustard has since spent time with the New Zealand Warriors rugby league team and oversaw an England training session with professional judo coaches on Monday.
"I was looking at league's defensive systems and stuff around the tackle," Gustard said.
"There are transferable skills from judo. We missed 80 tackles in the series against Australia and that's not good enough."
England host South Africa, Fiji, Argentina and Australia in November and December in the Autumn internationals.
(Reporting by Ian Rodricks in Bengaluru, editing by Ed Osmond)