But after coach Warren Gatland gambled with nine changes to his team, Wales looked far from Six Nations champions and must now produced something extraordinary against Ireland in Cardiff next week to retain the title.
Jones said: "We would obviously love to win the Championship but the first port of call is the Triple Crown which we can still win.
"Wining the title again would be special because we've shown character to bounce back after a defeat to France. But it's looking out of our hands now."
Wales went into yesterday's game with one eye on bettering Ireland's 38-9 win in Rome last month. But they were fortunate to win after Andrea Marcato kicked Italy to within eight minutes of a shock win.
Jones said: "There were mixed emotions after the game. We're obviously delighted to win this Test match but we know we were far from the complete package.
"We would have been a lot happier with a better points margin, but winning matches come first and that's what we did. We'll just have to see how other results go to see what will be decided next week."