Various newspapers and online publications circulated the image of Three Lions assistant manager Steve Holland holding a piece of paper which appeared to reveal the starting XI for this weekend's World Cup clash with Panama.
Southgate has insisted that paper was merely a squad list, rather than his final XI, but he warned the press to think twice before publishing sensitive information from the England camp.
"Obviously any time, if we were to give the opposition the opportunity of having our team it's a disadvantage to us," BBC Sport quotes Southgate as saying.
"So of course our media has to decide if they want to help the team or not."
England defender Kyle Walker has also spoken out against the leak, claiming that it is "not going to help us".