The victory was the biggest winning margin and highest number of points scored in matches between the two.
“Our aim is to be the best side in the world, it always has been,” Jones told BBC Sport.
“Are we moving in the right direction? Yes. Are we ready to win the World Cup now? No.”
After running in eight tries against Ireland, England have nearly two weeks before they play Italy in their final warm-up match on 6 September at St James’ Park.
Jones said that he is focusing on improving on England’s failure to get out of their pool at the 2015 tournament.
“The only thing we are worried about are [Pool C opponents] Tonga, USA, France and Argentina. We have to get through those games,” he added.
“The World Cup is about taking each game at a time and that is our only focus. They are the only teams in our mind.”
England’s first World Cup match is against Tonga in Saporro on 22 September.
Jones said he was pleased by his players’ intensity in their win over Ireland, who would have climbed to the top of the world rankings with victory.
However, he suggested that the scoreline might reflect their differing levels of preparedness for the World Cup rather than underlying quality. It was Ireland’s second warm-up match while England have now played three.
“This was a performance for the 80 minutes but we don’t know where Ireland are in their preparation so it can be misleading,” he added.
Wing Joe Cokanasiga scored two tries, his fourth and fifth in just seven Tests, after putting in an indifferent performance against Wales a week ago.
“It is important for young players to do that,” said Jones.
“If they have a bad game they learn, they have to make sure they bounce back in the next game. He did that and used his strengths really well.”