England travel to the Italian capital knowing it will be their only trip away from Wembley as they look to clinch a place in the semi-finals against the Czech Republic or Denmark.
The Three Lions lifted the nation by defeating Germany on Tuesday, but Southgate is keen his players retain their “edge”.
Southgate said: “It’s Saturday now for us, the messages are great, the congratulations are great, but they’re also dangerous because it can take an edge from you and we’ve got to get that edge in our feeling now to get back into performance state.”
England will know who they could face in the last four before their game at the Olympic Stadium against Ukraine kicks off at 8pm on Saturday as Denmark’s quarter-final against the Czech Republic is a 5pm kick-off in Baku.
The quarter-finals in the other half of the draw take place on Friday as Switzerland face Spain in St Petersburg (5pm) before Belgium take on Italy in Munich (8pm).
Post of the day
Italy have set a new national record of 31 games unbeaten going back to October 2018, beating the mark set by Vittorio Pozzo’s World Cup and Olympic champions of the 1930s. That includes wins in their last 12 games, without conceding a goal until Austria’s extra-time consolation on Saturday.
Their opponents are not far behind, though – Belgium are 13 games unbeaten, winning 11, and have lost only to England in the Nations League since the start of 2019. In 27 games each in that timeframe Italy have won 24 and drawn three, scored 80 goals and conceded seven, compared to Belgium’s 23 wins, three draws and one loss, 81 goals scored and 15 conceded.
Belgium’s key players Kevin De Bruyne (ankle) and Eden Hazard (muscle strain) are both injury doubts for their side’s clash with Italy in Munich and coach Roberto Martinez will make last-minute decisions on both.
Italy skipper Giorgio Chiellini is back in contention after missing his side’s previous two matches – wins against Wales, in their last group match, and against Austria.
Spain coach Luis Enrique has reported no new injuries for his side’s last-eight game against Switzerland, who will be without suspended captain Granit Xhaka after the Arsenal midfielder received his second booking of the tournament in the thrilling penalty shoot-out win against France.
Quote of the day
Switzerland v Spain (Quarter-final, July 2, St Petersburg, 1700 BST)Belgium v Italy (Quarter-final, July 2, Munich, 2000 BST)