Ireland, who had also ended New Zealand's run, won 13-9 at a rainswept Lansdowne Road on Saturday to deny England a 19th successive Test win and prevent them becoming the first side in the Six Nations era to win back-to-back Grand Slams.
Irish lock Iain Henderson scored the only try of the match, although England's defeat came after they had already retained the Six Nations title.
The British and Irish Lions travel to New Zealand for a three-Test series in June and July.
England, by contrast, are not scheduled to face the world champions until 2018, although reports this week suggested officials were looking at re-arranging the Twickenham fixture calendar to set up a November 4 clash between the international game's two top-ranked teams.
"I expect at least 15 of our guys to go on the Lions tour, I'd be disappointed if we don't have that many guys in," said Jones after suffering his first defeat in 18 Tests as England coach.
"And I think they'll have a massive shout (of winning a first series in New Zealand since 1971).
"New Zealand, as Ireland have shown, are there for the taking," the Australian added in a reference to Ireland's 40-29 win in Chicago in November that stopped the All Blacks' run at 18 victories in a row.
"I can can't wait for us to play them either.
"We're very keen to play them, I've had a discussion with Ian (Ritchie, the chief executive of England's Rugby Football Union) and we're raring to go."
However, with the Lions squad not announced until April 19, Jones added: "There's a lot of discussions to go."
Before the match, Jones had suggested Ireland might play a 'kick and clap' game.
Ireland, understandably took issue with the implication they had a limited approach.
But in classic 'Irish' rainswept conditions, it was the hosts who produced the superior wet-weather rugby.
"Ireland played superbly and they were too good for us on the day," said Jones.
"We're all human beings, we're not perfect, and that's why world records finish at 18 games because it's hard to keep going.
"They used the conditions superbly, we probably didn't."
Meanwhile Jones dismissed talk the loss had lifted a weight from England's shoulders, saying: "No, I think it's fantastic having the pressure to perform.
"To win the World Cup you've got to win seven in a row, you've got to cope with that pressure.
"That was like a World Cup final today and we weren't good enough."
Jones, appointed after England's World Cup flop on home soil two years ago, has long made it clear his ultimate goal is to win the 2019 edition in Japan.
"We're 14 months into a four-year project," he said. "Full credit to Ireland, they were brilliantly coached and executed their plan well.
"We'll have more setbacks as we move towards the World Cup," he added after England were denied a Grand Slam in Dublin for the third time since 2001.
Both Ireland and England were captained by potential Lions skippers in hookers Rory Best and Dylan Hartley respectively.
Ireland coach Joe Schmidt, asked whether his fellow New Zealander Warren Gatland, the Lions boss, should pick Best as captain of the combined side, replied: "My choice doesn't count for anything, so I don't really express it.
"I'm incredibly proud of him (Best) and the way he leads the team. I'm delighted he's our leader."