The English play Ireland in Dublin on Saturday with a chance to become only the sixth team in championship history to win successive Grand Slams.
Care, who scored two of England's seven tries in their 61-21 mauling of Scotland, said: "We have gone to some big places and won big games". "There is failure on the one side or we can kick on, get better and hit those lofty heights that he [Jones] is talking about".
Jones also touched on comments made by England's World Cup-winning coach, Sir Clive Woodward, who expressed his belief that anything less than the Grand Slam would constitute a failure for the pre-tournament favourites and No 2 ranked side in the world.
"The performance against Scotland was pretty ruthless so it was a good progression for the team, but we've only equalled New Zealand's record".
"We'll have a couple of quiet drinks tonight and enjoy that and attention then turns to Ireland and that's going to be hard".
"We want that record".
Beaten by Scotland on the opening day, Ireland's defeat in Cardiff was their second in 2017 and their eighth in 17 matches since topping their 2015 World Cup pool.
"We have got to be more aggressive, more emotional in the right way, more committed, as well as smart and skilful. But we've got something to aim for". "A lot of our boys have been down there so we have some experience".
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What they're really waiting for now is a second straight Grand Slam. "It's very humbling to get them cheering me like that, although I believe it was more for Nathan Hughes coming off because he had a stormer", he added modestly.
It was Vunipola's first global appearance of this Six Nations after he suffered a knee ligament injury back in November.
Shaun Edwards was disappointed to have been accused of a rude gesture while celebrating Wales' Six Nations win over Ireland.
On an afternoon where fans basked in the glory of an England side delivering a highlight reel performance, they were also treated to a veritable love-in from Hartley and Joseph.
"Last year we were nervous and I expect us to be nervous this year", he said.
"This is great for us".
"We are positive Elliot is going to be okay".