The Magpies boss was fined £100,000 by the club and has also been charged by the FA over the incident, and Southgate believes that he could be better served sitting in the stands to avoid anything similar happening in the future.
"As a coach, you always ask yourself how close do you need to be? Do you need to be in constant contact with the team? Would you not have a better view of the game from up high or do you simply believe you have to be there because the supporters need to see you?" Southgate told Sky Sports News.
"You do like to be able to connect with your players, and there may be times when they need you during the games, but what you don't want to do is play the game for them. With these U21s I would hope to intervene minimally from the sidelines because you work through the week and try to prepare them as best as possible for games.
"But as you get older you may see different things which are key to that relationship between you. But we have to trust them to go and play and make sure we don't interfere too much."
Pardew has been given until 6pm on Thursday to respond to the FA's charge.