Jones, 24, said: "It was one of the most stupid and idiotic acts I have ever done on a rugby field and I thought it would jeopardise my international career. You have to have that view when you make such a mistake because the opportunities to play Test rugby are few and far between.
"I am fortunate but I've been given this second opportunity now. I don't want to try too hard because that's when you make silly mistakes but I obviously want to put some wrongs right."
Wales assistant coach Shaun Edwards confronted the British Lions second-row star in the dressing room following the costly sin-binning and warned him never to repeat his actions.
But Kiwi coach Gatland believes the incident at HQ has been put firmly behind them. Gatland said: "It was dealt with straight away in the dressing room and is dead and buried.
"Everyone makes mistakes and I'm sure he and the other players will learn from it. Sometimes you get away with having 14 men but we didn't."
But Jones accepts the Welsh management were correct to single him out for punishment. He added: "Shaun and Warren were right with what they said. When Warren first came in he said he would be honest with the players. It is refreshing and I respect him for saying it.
"It's a cut-throat mentality we haven't had before and Gats has brought that off-field southern hemipshere cutting edge. Hopefully that will provide dividends for us."
Gatland has made just two changes for the clash at the Millennium Stadium with wing Leigh Halfpenny and line-out specialist Jonathan Thomas preferred to Tom James and Luke Charteris with fit-again prop Gethin Jenkins on the bench.
Gatland said: "Jonathan is experienced and will bring us some extra mobility while Leigh offers us an extra kicking option."
Wales: L Byrne; L Halfpenny, J Hook, J Roberts, S Williams; S Jones, G Cooper; P James, G Williams, A Jones, AW Jones, J Thomas, A Powell, R Jones (capt), M Williams
Replacements: G Jenkins, H Bennett, B Davies, S Warburton, R Rees, A Bishop, T Shanklin