The England coach vented his frustration during the second half, with television cameras showing him slamming down a notebook in the coaches' box in the second half and mouthing two successive expletives.
"I'd like to apologise for swearing in public," Jones told reporters at England's training base in Bagshot on Monday.
"It's not acceptable so I apologise for that and I'll find a different way to express my frustration in the future," the Australian added.
Victory saw England make it 20 wins in 21 Tests under Jones, the only blot on the former Australia and Japan coach's Red Rose record a defeat by Ireland in Dublin in March that denied them a repeat Six Nations Grand Slam.
As for a faltering display against the Pumas, Jones said he had to carry the can.
"I thought our effort and application were first class. Argentina are a difficult team, but I obviously didn't coach the team well enough," Jones said.
"It's my fault the team didn't play well so I take full responsibility for that," he insisted ahead of England's match against his native Australia at Twickenham this coming Saturday. "I just didn't coach them well enough."
Meanwhile England fullback Mike Brown could yet feature against the Wallabies despite landing heavily on his head and going off in the 22nd minute following an aerial challenge with Joaquin Tuculet that saw his Pumas counterpart shown a yellow card.
Two years ago, the Harlequins No 15 had a lengthy spell on the sidelines after being knocked out against Italy.
"Mike is doing really well," Jones said. "He did some bike today (Monday). There are set protocols on return to play and he's progressing pretty well. I'd think that at this stage he's still in contention.
"The medical staff are very in tune with the players' welfare. That's at an absolute premium and that's the first thing we take into consideration."
Against Argentina, Anthony Watson moved across from the wing to fullback when Brown went off.
"Anthony went very well," said Jones. "He hadn't trained there, so it was a really good exercise."
Jones, Australia's coach when they lost the 2003 World Cup final to England in Sydney, is aiming for a fifth straight victory over a Wallabies team coached by Michael Cheika, his former team-mate at Sydney club Randwick.
"Australia were beaten by 50 points in the first Bledisloe Cup game and the second one they won," Jones said. "They've really turned it around through some very good coaching.
"Their selection has been good, their defence is very good, their set piece is strong.
"They're playing some good rugby and are probably the form team in the world at the moment."