Jones was full of praise for Japan, the team he coached to their famous World Cup win over South Africa in 2015 and who host the tournament next year.
The arrival of Owen Farrell as a halftime substitute helped to change the flow of the game, though, and the English scored all of their points from the 56th minute - through three tries and 10 points from flyhalf George Ford - to survive a scare.
Mark Wilson's first worldwide try put them back in front, then Cokanasiga and Dylan Hartley went over as England finally clicked into gear with a clash against Australia to come next weekend. "Maybe we got seduced after scoring an easy try in the first few minutes", he said. "The stats of the first half were probably reversed".
"Owen Farrell made a difference for our team because he's an influential player".
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England turned around a 15-10 half-time deficit, scoring four tries in their victory, and Jones was pleased with their second-half performance as well as the challenge Japan posed.
"The players subconsciously think it's going to be easy and that showed in our attitude and effort, which was disappointing".
Elliot Daly levelled matters with a long-range penalty but the powerful Michael Leitch had the final say of the first half when he got the better of some desperate tackle attempts to score his side's second try.
Yu Tamura booted a penalty to reward Japan's endeavor and after England hooker Jamie George was sent to the sin-bin, England center Alex Lozowski failed to stop Ryoto Nakamura as the center ran hard for the line from a five-metre scrum.
They could and should have had more as their quick thinking and sharp handling constantly had England on the back foot and pinned into their own half.
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In the first half Japan had 77 percent of territory and 69 percent of possession.
And Jones has hailed Farrell, who came off the bench, for his impact against Japan.
The scoreboard looked respectable in the end but there was little to celebrate for England, who complete their November programme next Saturday against Australia, who beat Italy 26-7 earlier.
"It was a big experience for us and it's exactly what we need as we get into the World Cup next year", the former New Zealand global added. "We weren't getting stuck in but started doing that in the second half". "We played some really positive rugby and, most of the time, matched the physicality", he said.
Current Japan coach Jamie Joseph was also happy with the display, though disappointed at the way the team faded.
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England forward Maro Itoje: "Against any team in worldwide rugby we know the opposition will have quality and Japan had a lot of quality, they didn't give up".