The 28-year-old was handed the responsibility after Warburton, the tour captain, injured his hamstring in the second Test.
The flanker returned to fitness in plenty of time to captain Wales this year only to suffer a shoulder injury at the end of Saturday's victory over Scotland.
Warburton's latest blow could rule him out of Wales' summer tour of South Africa, clearing the way for Jones to take the armband but he is not thinking that far ahead.
"I never worry about stuff like that," he told WalesOnline.
"Ultimately, I have to be playing good rugby, finish the season fit and deal with what I have to deal with domestically.
"We can be happy with three home wins, but obviously we are bitterly disappointed with the two away losses and performances.
"Ireland was massively disappointing because we didn't get our game going, then against England we didn't take our opportunities.
"So it was a bit of mixed bag, but a few years back we probably would have been happy with three home wins."