Wales edged out the Pacific Islanders 17-13 at the Millennium Stadium thanks to a try and penalty from Leigh Halfpenny and nine points from 20-year-old outside half Dan Biggar.
But they were forced to hang on in a desperate last ten minutes after London Irish centre Seilala Mapusua pounced on a wayward Biggar pass to sprint clear from his 22 to the posts.
"It was about as tough as it gets in Test match rugby. The Samoans gave everything and really hit hard but our boys dug deep for the victory that we wanted and needed," said Jones.
"There is a courage, strong work rate and work ethic with my guys and it was great we kept them out in the last five or six minutes.
"But we need to look at cutting out the mistakes. We have been offering so much, but not quite delivering - we haven't had that clinical edge in our game.
"It has been a case of the last pass or the last phase letting us down. But, fair play to the Samoans, they came together on Sunday and put a fantastic performance together." Wales coach Warren Gatland was as frustrated as his skipper at the performance and pin-pointed the glut of kicking in the first half as part of his sides failing.
"We have to learn from our mistakes and in the first-half we kept kicking the ball away," admitted Gatland.
"We wanted to be more ruthless in our approach, but unfortunately we weren't. We created a lot of chances and line breaks and we should have put the game away."
Wales move on to play Argentina in Cardiff next week, on what will be a newly laid Millennium Satdium turf following the announcement that the current, troublesome pitch has been contaminated by Bibionidae Fly infestation.
For their part, Samoa move on to Paris to take on the French. That is a game that skipper George Stowers says his side are looking forward to even more after their close shave in Cardiff.
"The boys can be very proud of themselves for pushing a top tier nation so close. It was a case of so near, yet so far, but our performance shows we deserve more games against the big teams, especially after only a few days together," said Stowers.
"For many of us it was the first time we had played Wales, so this was a great heads-up for where we are against the best teams. Against France next week we have to be smart, keep our discipline and play for the full 80 minutes, as well as putting in the big hits."
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