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The 84-year-old entertainer was convicted of 12 counts of indecent assault against four girls, one of whom was as young as seven or eight.
He is likely to be jailed at his sentencing on Friday.
"I feel gutted and dismayed but it's very important that we do everything we humanly can to protect vulnerable young people," Mr Abbott told ABC radio.
The assaults took place in the UK between 1968 and 1986.
The main complainant was a childhood friend of Harris's daughter Bindi.
Harris was also found guilty of assaulting Australian woman Tonya Lee at a London pub in 1986 when she was 15.
"Sexual abuse is an utterly abhorrent crime," Mr Abbott said.
"It's just sad and tragic that this person who was admired seems to have been a perpetrator."