The disappointing performance in Friday's goalless draw with Scotland has led to calls from pundits and fans for Southgate to adopt a more positive style.
In a separate statement, the ministry also announced the expulsion of three Slovak diplomats, who must leave by May 5, and accused Bratislava of "false solidarity" with Prague.
Russia retaliated by ordering out 20 Czech diplomats -- sparking an angry ultimatum from Prague for Moscow to let them return or face further expulsions from its embassy.