Last season 11 United fans ended up in hospital after attacks by fans and baton-wielding riot police.
"In fact, when you saw some of the scenes, it was amazing no one was killed. So hopefully that's an instant reminder to us, just seven or eight months later, that there needs to be good behaviour.
"There needs to be good behaviour from our fans, of course, who I don't think did a lot wrong from what I gather.
"But they will have to be absolutely vigilant about their behaviour, not to be intimidated, go to watch the game and enjoy it. That's what we expect them to do."
Ferguson slammed the riot police for being only in the United end of the ground for the quarter-final first leg last season.
He added: "What disturbed us when we watched the video footage, was that all the police were in the Manchester United section.
"There were no police in the Roma fans' section so they could hurl all sorts of objects at our fans.
"There was some story that the Rome police were scared to get among their fans. I find that quite incredulous. I think they should be keeping control of both sets of fans."