In the build-up to the Group C clash, photographs emerged of England assistant coach Steve Holland holding a sheet of paper with the apparent line-up on it.
Journalists have faced criticism for publishing the contents of the sheet but Southgate says he is unfazed.
"There's no drama," Southgate told reporters on Saturday.
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"The picture the other day wasn't even the team so it was even less of a drama, it was a list of runners and riders for the training session. I am totally relaxed.
"I understand a few of the guys (British media) have had a bashing on social media. Sorry for that and I don't wish that on anyone as I have had it myself."
Reports of England's team also came out in the British media ahead of their first World Cup game against Tunisia and Southgate believes it is just something his team have to live with.
"The team came out three days before the first game and I didn't say anything because it's something we can't control," he said.
England went on to win that game 2-1 and currently sit second in the group, three points behind leaders Belgium.
"I don't expect the media to be supporters of us in the way they work," added the former defender.
"They want us to do well, that's been clear throughout the tournament."
(Reporting by Jack Tarrant; Editing by Ian Chadband)
