Bellingham was fined 30,000 euros ($32,470) and handed a one-match ban that was suspended depending on good behaviour for one year after a crotch-grabbing gesture following England's 2-1 win over Slovakia in the round of 16.
He scored a stunning bicycle kick to equalise late in normal time that helped keep England in the tournament, and an immediate suspension would have been a big blow to Southgate's team.
"I thought it was a commonsense decision," Southgate said on Friday on the eve of England's last-eight clash with the Swiss. "When you score a goal of the quality that he did, at the age that he is, you are going to get a rush of adrenaline."
Bellingham, who has scored two of England's four goals in the tournament, said his gesture was a laugh with friends. European soccer's governing body UEFA said it was "violating the basic rules of decent conduct."
"There was no intent in the gesture towards anybody but communication he has with his family," Southgate said. "From our perspective we thought it (the punishment) was a sensible outcome."
Asked if he had spoken with the Real Madrid midfielder about the incident, Southgate said: "I speak to our players all the time so don't feel the need to spend extra time with Jude. He is aware of the investigation and he is an intelligent guy."
England goalkeeper Jordan Pickford added: "Just let him play his football and enjoy it."
Bellingham's punishment did not sit well with some Turkey fans after their team's defender Merih Demiral was handed a two-game suspension that will keep him out of Saturday's quarter-final against the Netherlands.
Demiral mimicked the shape of a wolf's head with his fingers after his second goal in Turkey's 2-1 win over Austria in the last 16. The symbol has been linked to Turkey's far-right "Grey Wolves" group and was condemned as racist by Germany.
UEFA said Demiral was punished "for violating the basic rules of decent conduct, for using sports events for manifestations of a non-sporting nature and for bringing the sport of football into disrepute".