Andrew Soper (also known as Father Laurence Soper) said his whole life had been "ruined" by the allegations over to his time as headmaster and senior priest at fee-paying St Benedict's School in Ealing, west London.
While on police bail over accusations dating back to the 1970s and 80s, Soper went on the run in Kosovo - but was extradited back to England face trial at the Old Bailey.
Ten former pupils have made allegations against him, including that he used the cane as a ruse to sexually assault and rape them.
Jane Humphryes, QC, defending, asked the defendant: "Have you ever sexually assaulted any of the complainants from this trial?"
The former Ealing abbot replied: "Never."
His lawyer asked him to explain why he fled Rome for Kosovo while under investigation by police in Britain in 2011.
He said: "My stupidity and cowardice and wishing to bury my head in the sand played a big part.
"If you want to destroy a priest, vicar, anybody, all you have to do is make an accusation up against them. Their future is ruined, their character is ruined.
"Their past is ruined because the whole thing is re-interpreted - everything you have done in the past and tried to do for good - in sexual terms. You must have been in it for something.
"By the time I fled on March 4 2011, I had been on police bail for six months and I had a phone call from a solicitor in England saying I was going to be re-bailed for another three months.
"The pressures I suppose on anybody being on police bail under that suspicion is quite considerable."
The 74-year-old told jurors he had been having doubts about his vocation as a monk for about 10 years, but insisted he never went to Kosovo because he was guilty.
Ms Humphryes asked if Soper had become a teacher so that he could start "monstrously" abusing boys, as was claimed by one of the alleged victims - who cannot be identified for legal reasons.
Soper replied: "Certainly not. What he said horrifies me. I was not the one that did it, if it did happen. Simple as that."
The defendant told jurors he had been beaten with a cane several times when he was a pupil at St Benedict's in the 1950s and it was "not totally uncommon" to hear of others to be caned with their "clothes off".
As a teacher, Soper told jurors he had caned boys and had been concerned at the time not to change the discipline code amid fears that things would "start to fall to pieces".
But he felt "totally different" about the practice now, and denied he had ever caned anyone behind locked doors.
Soper said he had been on first name terms with Cardinal (Basil) Hume and knew old boy Lord Chris Patten, who worked on the advisory panel while he was Abbot.
He denies the 19 offences of indecent assault, indecency with a child, and buggery allegedly committed against 10 boys in the 1970s and 80s.