Team-mate Rio Ferdinand was struck by a coin near his eye following Robin van Persie's late winner, before a Manchester City fan entered the pitch to confront the centre half.
The incident is being investigated by both the FA and Greater Manchester Police, with the fan in question - 21-year-old Matthew Stott - facing a lifetime ban from the ground if found guilty in court of a charge of pitch encroachment.
When Ferdinand, who was able to complete the match, left the pitch after the final whistle he was seen to have an object in his hand which he showed to referee Martin Atkinson before he threw it to the ground.
Giggs watched the incident unfold from the bench and can understand the anger felt by Ferdinand, having himself been in a similar position in the past.
"No it's (the incident) is not isolated," he told United's official podcast, Red Voices.
"The manager touched on it. I got hit at Chelsea when Chicharito scored.
"It happens. I think it's tough for someone to get hit in the face, for everyone to sort of make a big a thing out of it.
"It's not just one club, it's not just City, it's not just Chelsea. Every club, the excitement and the passion we all want but we don't want it to tip over the edge.
"A centimetre either side and Rio loses an eye, it's so dangerous. We don't want to see it. It is up to the clubs and the police, the FA to do everything in our power to make sure it doesn't happen again."
Ferdinand has been criticised for celebrating Van Persie's winner in front of the home fans, but Giggs feels the way the supporters are segregated and the importance of the goal makes it almost impossible not to do so.
"First of all it's tough at City because their hardcore supporters are right next to our supporters," he added.
"When they are so close together how can you determine whether you just celebrating in front of United fans?
"When you score a goal like that you don't have control of yourself. As a player you want to celebrate.
"If you just scored that goal and walked back to the centre circle, United fans would want to know 'what's going on there?'. The manager would be like 'what you doing? Celebrate'.
"We have stamped it out going into the crowd, you get an instant booking.
"You have still got to enjoy that sort of experience, but obviously the players and fans can't go too far."