O'Neill, who took over at the Stadium of Light earlier this month following the departure of Steve Bruce, was given a headache last week after the arrests of captain Lee Cattermole and Nicklas Bendtner for alleged criminal damage.
O'Neill said he would await the result of a police investigation before deciding what action to take against Cattermole and Bendtner.
However, O'Neill stressed the importance he placed on Sunderland players setting a good example.
"The police have to finish their inquiries, but it's a very serious issue and it's one that wouldn't be overlooked by the football club," he said.
"We do have some responsibility here. Players and managers, I believe, have extra responsibilities now at football clubs.
"My own view is that behaviour on and off the field is of paramount importance, decent behaviour.
"The expectation as well, particularly of footballers now in this league, where they are in a very nice position financially, they kind of owe a debt, and that's something we would like to see happening at this football club."
Source: AFP
Source: AFP