The panel absolved Liverpool supporters of blame for the Hillsborough stadium tragedy of April 1989, when 96 people attending the FA Cup semi-final between Liverpool and Nottingham Forest were crushed to death.
Speaking at his regular Friday press conference, Sir Alex expressed his hope that Hillsborough - and, in turn, United's plane crash at Munich in 1958 - will no longer be referenced in taunts between rival supporters. In nine days' time, his team will be the first to play against Liverpool at their Anfield home since the panel's report was made public.
"It shouldn't need what happened this week to change things [between United and Liverpool supporters]," said Sir Alex.
"Two great clubs like ourselves and Liverpool should understand each other's problems. The fact we're playing them after the findings we've been reading about in the last few days does bring a focus to it.
"Both clubs have suffered such tremendous fatalities through football. Maybe this will be a line in the sand now in terms of how supporters behave towards each other. The reputation of both clubs doesn't deserve trouble. You hope supporters of both teams support their club and that's the end of it."