England triumphed 1-0 over Switzerland in an worldwide friendly at Leicester City's King Power Stadium.
Rashford is again struggling for game time at Old Trafford this season, but Southgate says his performances for England this week will boost his confidence when he returns to club duty under Jose Mourinho.
Marcus Rashford went into the global break under a cloud, after being red-carded for rashly lowering his head into Phil Bardsley's face during Manchester United's 2-0 win at Burnley, but he emerges from it as one of the few players to have scored points - and the only one to have scored any goals - for England. Delph offered little forward thrust either, meaning that it was often left to Rashford to take the initiative by turning and running at the Swiss back three.
I'm concerned about Harry Kane.
Southgate also reserved praise for Rashford, who built on his goal against Spain at the weekend with a tidy finish to win Tuesday's game after what has been a frustrating start to the season for the Manchester United youngster.
Rashford scored in England's matches against Spain and Switzerland, moving onto five worldwide goals.
Rashford will not play in United's next three domestic matches after being sent off in a 2-0 win at Burnley earlier this month. We needed to keep him ticking over. I think they might, at the beginning, let Tottenham come at them a little bit, give them a bit of respect, which is right because Tottenham's home record was great previous year. There is huge competition for places at his club so you can understand that.
"I was delighted [with Rashford] because we really wanted to make him feel important over this period", Southgate said. "He's a huge admirer of him, but he's got his job to do", Southgate maintained.
"We have to remember that I don't think Harry, at that age, had hardly played anywhere near the matches for Spurs, really". It was his second goal in two games for the England team. Television footage of the players walking out onto the pitch was broadcast in black and white for 25 seconds to mark the 25th anniversary of the anti-racism campaign Kick It Out.