Smith stood down from his post as captain and was banned for one test match by the International Cricket Council (ICC) on Sunday after admitting conspiring to tamper with the ball during the third test against South Africa in Cape Town.
Unsourced media reports in Britain have said that some England players had suspicions over whether Australia had doctored the ball during their 4-0 series victory, but Root quickly knocked that down on Monday.
"Not to my knowledge. I was not aware of any ball tampering," Root told reporters in Auckland after his side crashed to an innings and 49-run loss to New Zealand in the first test.
"I have enough to worry about... but it's disappointing for test cricket and cricket in general."
England pace bowler Stuart Broad had also said that he was unaware of any tampering by Australia's bowlers, despite the fact they were able to get reverse swing in conditions that were not usually conducive to being able to do so.
Root added that while the burden of responsibility for teams' behaviour always fell upon the captain, some of it rested with the players themselves.
"As captain you're responsible for how everyone else behaves," he said. "I have to look after my own group and make sure I'm happy with how they conduct themselves.
"As an international player you should know the rules. I should not have to back that up. It's as simple as that."
(Reporting by Greg Stutchbury; Editing by Christian Radnedge)
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