The five-time world champions dominated the game and England goalkeeper Joe Hart made several fine saves.
England fought hard but could muster few efforts on goal, though Marcus Rashford, Eric Dier and Dominic Solanke all went close. But the England coach was delighted that his young team – with Liverpool rookie Joe Gomez outstanding – ground out a gutsy draw against the team ranked No2 in the world, just four days after holding the world No1’s, Germany, by the same score.
Southgate said: “In terms of heart, resilience and spirit it was up there with anything I’ve been involved in.
“We couldn’t get hold of the ball and keep it. Tonight we just showed resilience, guts and some outstanding defending and I’m incredibly proud.
“We had the best defensive record in Europe in qualifying and we’ve played the best two teams in the world and not conceded.
“When you dig in you get half chances and we had them at the end and could have won the game. It’s a base to work from.
“Joe Gomez’s performance against top players – like all of the defending – was outstanding. It was a top performance.”
Gomez, who looks like another find for Southgate after the emergence for England recently of Harry Winks and Ruben Loftus-Cheek, said: “We put in a good shift and we’re happy with that. It’s a great honour, I’ll keep trying to improve and hopefully more of these days will come.”
Hart said: “The back line were phenomenal. Joe Gomez played against one of the best players in the world and was excellent. We have played two of the best teams in the world, we didn’t win, but we didn’t lose.”
England’s defence, led by 20-year-old Gomez, held out well under constant Brazilian pressure, with Neymar, Gabriel Jesus, Paulinho and Philippe Coutinho all starring.
The closest Brazil came was when Fernandinho clipped the post late on.
Meanwhile, Antonio Conte is wanted to revive Italy after the humiliation of failing to qualify for the World Cup.
Conte is the preferred choice of some senior Italian FA members to return and replace Gian Piero Ventura, but Carlo Ancelotti and Roberto Mancini are also in the frame after the disastrous playoff defeat to Sweden on Monday.
The Chelsea boss led Italy to the quarter-finals of Euro 2016 before moving to Stamford Bridge.
Ancelotti is available after his sacking by Bayern Munich but has said he wants to take the rest of the season off. Ventura is expected to learn his fate today.
England face the Netherlands and Italy in friendly games in March.