Southgate said that the players and staff had discussed the issue but suggested that, if there were incidents, leaving the field was not likely to be an option.
A makeshift England side beat Romania 1-0 in their final Euro 2020 warm-up game, while Belgium's Romelu Lukaku underlined his status as one of the world's top strikers with his 60th international goal to secure a 1-0 win over Croatia.
Zidane plays down Ronaldo injury; Liverpool's Gomez sidelined after surgey
France stretched their unbeaten run against Croatia to eight games after a late goal by Kylian Mbappe gave the world champions a 2-1 win in their Nations League top-tier Group 3 match on Wednesday.
Tottenham Hotspur's England duo Harry Kane and Dele Alli fired them to a comfortable 2-0 win over mid-table Watford that cemented their place in the top four at Wembley on Monday.
Stoke thought they had secured all three points and their first away win since October when substitute Peter Crouch knocked a loose ball into the back of the net after West Ham's England goalkeeper Joe Hart spilled a shot after 79 minutes.
Liverpool survived a late spell of Everton pressure to stretch their record unbeaten run in Merseyside derbies to 17 games
A summary of Friday's Euro 2020 qualifying matches.
The following are talking points from the weekend's Premier League action:
Real Madrid captain Sergio Ramos risks being hit with an extra game suspension which would rule him out of a potential Champions League quarter-final first leg after admitting he got booked on purpose in Wednesday's 2-1 win at Ajax Amsterdam.
News of all that's transpired on and off the football field
Croatia ruthlessly exposed England's limitations in the second half of the World Cup semi-final on Wednesday as Zlatko Dalic's side fought back to secure a famous 2-1 extra-time victory.
England forward Jamie Vardy is "looking doubtful" for the World Cup quarter-final against Sweden on Saturday after suffering a groin strain having come on as a late substitute in the last-16 win over Colombia, manager Gareth Southgate has said.
Stones headed England in front in the eighth minute, losing his marker to angle home a Kieran Trippier corner before captain Kane made it 2-0 in the 22nd minute with his third goal of the tournament, an emphatically struck penalty after Jesse Lingard was pushed over in the box by Fidel Escobar.
England manager Gareth Southgate may be recovering from a dislocated shoulder suffered while jogging, but he may run into more discomfort when deciding whether to drop Raheem Sterling for Marcus Rashford in Sunday's World Cup game against Panama.
Joe Maguire was found guilty of repeated bodily harm, violence against public employees and attempted bribery. Sharman was found guilty of insult, repeated bodily harm and violence against public employees.
Uruguay will head to the World Cup on a winning note after beating Uzbekistan 3-0 in a chilly warmup in front of their own fans on Thursday.
Germany's Lukas Podolski capped his international swansong with a sensational goal to give the world champions a 1-0 victory over England in a friendly on Wednesday.
Images from the World Cup qualifying matches played on Wednesday night.
Southgate hopes Black Lives Matter protests could signal change in society
Images from the FIFA World Cup qualifiers matches.
An emotional and apologetic Sam Allardyce said on Wednesday an error of judgement had led to his shock exit as England manager following a newspaper sting.
Images from the Champions League football matches played on Wednesday night.
After more goals came from set-pieces in this World Cup's group stage than any other, dead-ball strategy has continued to have a huge impact in the knockout phase, with five of the 11 goals scored in the quarter-finals coming from free kicks or corners.
Analysis of the eight groups for the 2018 FIFA World Cup to be held in Russia.
Four years ago in Brazil, Colombia romped to the quarter-finals for the first time on the back of four straight wins, salsa-dancing to celebrate their dozen goals and launching midfielder James Rodriguez on the road to global stardom.
Morocco winger Nordin Amrabat has been discharged from hospital but he will not play in the side's next World Cup Group B clash against Portugal on Wednesday after suffering concussion in the 1-0 loss to Iran, officials said.
However, experienced goalkeeper Joe Hart and Arsenal midfielder Jack Wilshere were both omitted from a squad announced on Wednesday via a social media video featuring young recreational players from around the country shouting out the names.
Spain began a new era under Luis Enrique in impressive fashion as they came from a goal down to outplay England in a 2-1 win in their Nations League opener at Wembley Stadium on Saturday.
France earned a rollercoaster 4-2 home win over Croatia in an entertaining top-tier Nations League Group 3 match, while England were held to a 0-0 draw by Denmark in an uninspiring game.
England soccer coach Roy Hodgson's four-year reign came to an abrupt end after their shock 2-1 defeat by tiny Iceland at the Euro 2016 round of 16 stage on Monday.
News of all that's transpired on and off the football field.
England's right-back Kieran Trippier is one of the World Cup's top performers.
Southgate's formation and tactics have been hailed as progressive and modern, there is also something traditionally English about the team's strengths.
News of all that's transpired on and off the football field
Liverpool and champions Manchester City drew 0-0 at Anfield while Chelsea and Arsenal enjoyed comfortable away wins. City are top on goal difference from Liverpool and Chelsea with Arsenal two points behind.
News of all that's transpired on and off the football field
Striker Marcus Rashford scored a second-half winner as a young and much-changed England avoided an unprecedented fourth successive defeat by beating Switzerland 1-0 in a friendly on Tuesday.
News of all that's transpired on and off the football field
Marcus Rashford's penalty and a deflected strike from Mason Mount helped England come from a goal down to overcome top-ranked Belgium 2-1 at Wembley on Sunday and climb above them in their UEFA Nations League group.