For the second straight week, after a 19-16 win over France in their Six Nations opener at Twickenham, England snatched victory in the closing minutes.
England next play Italy -- thrashed 63-10 at home to Ireland earlier on Saturday -- at Twickenham on February 26 and Jones said: "We have used up all of our get out of jail cards and against Italy we don't want to be in that position again."
Jones, who has now won all 15 of his matches as England coach following his appointment after the hosts' first-round exit at the 2015 World Cup, said this latest victory demonstrated his side's growing resolve.
"We are a gritty team with characters in there that don't know how to get beaten and that was evident today." - Eddie Jones
Meanwhile Jones, who had upset Wales by insisting the stadium's retractable roof remain open, said he had relished his first Anglo-Welsh clash.
"It was a proper Test match with fans giving you stick throughout the game, great atmosphere and it reminds me of Suncorp Stadium in Brisbane, with fans close to the pitch and a fantastic atmosphere.
"Maybe we will close the roof next time," he joked. "They can close the roof now."
On a more serious note, Jones, sacked as Australia coach after a 2005 defeat by Wales in Cardiff, added: "I can not believe all the things that went on this week about the roof.
"The roof should be open unless the conditions are going to be absolutely terrible, that's how rugby should be played because it's a winter sport."
For Wales boss Rob Howley, whose side lost George North an hour before kick-off when the powerhouse wing failed a fitness test on a leg injury, thoughts of what might have been were scant consolation.
"It was an outstanding Test match," said Howley, whose side were 13-8 up at the break thanks to a try by left wing Liam Williams.
"But you have to execute under pressure and England did that better, which is why they deserved to win."
Wales were 16-11 in front with nine minutes left but an Owen Farrell penalty reduced their lead before left wing Elliot Daly went in at the corner for a converted try that extended England's national record winning streak to 16 victories.
A fast-paced first half ended with Wales five points in front at 13-8.
Leigh Halfpenny's boot appeared to have secured victory for Wales but England rallied to ensure their Australian coach Eddie Jones retained his perfect record as Red Rose boss.
The decisive passage of play saw Wales force a turnover near their own try-line only for centre Jonathan Davies's aimless kick to be run back in style by Daly, who beat Alex Cuthbert for pace for a stunning try.
Significantly, Farrell added the awkward conversion and that meant Wales had to score a try just to equalise. But England's defence held firm.
Just moments before his try, Daly had got back to end Wales fly-half Dan Biggar's 70-metre interception run.
"There wasn't much thought going through my head, I just ran to the line," he said.
Tries: L Williams. Cons: Halfpenny Pens: Halfpenny 3
Tries: Youngs, Daly Cons: Farrell Pens: Farrell 3
IRELAND vs ITALY
A hat-trick of tries for CJ Stander and Craig Gilroy, and nine conversions from fly-half Paddy Jackson, relaunched Ireland's Six Nations title hopes Saturday with a record 63-10 win over Italy in Rome.
Ireland, the 2015 champions, arrived in the Eternal City looking to make amends for a 27-22 defeat at Murrayfield when Scotland scored three tries in the opening half hour.
And Joe Schmidt's men left the "Colosseum" of the Stadio Olimpico with no doubts as to their tournament credentials.
Despite their loss to Scotland, New Zealander Schmidt was buoyed by a win that sets the Irish up well for France next week: "We didn't release the pressure valve."
"I thought we were a lot more clinical than usual," said Ireland No 8 Jamie Heaslip, standing in as captain after hooker Rory Best was sidelined by a stomach bug.
"We definitely held on to the ball better through the phases."
Although Italy made amends for a 33-7 defeat to Wales with far better discipline, Conor O'Shea's men were dominated for long periods and, worryingly, saw their defence collapse in a completely one-sided second half.
O'Shea, who played 35 times for Ireland as a full-back, had asked for discipline to improve after shipping 15 penalties to Wales.
But in doing so, Italy's game elsewhere suffered.
"In the first 20 minutes we took a battering," said O'Shea. "We talked about Ireland's ability to hold the ball through the phases, and the first 20 minutes took a physical and mental toll on us.
"We played against a team that, in every department, is better than us. It was a tough day.
"But we will never hang our heads. We have to get ready in one week's time and be focused for England at Twickenham."
Tries: Penalty Cons: Canna Pens: Canna
Tries: Gilroy 3, Stander 3, Earls 2, Ringrose Cons: Jackson 9