England's players required a half-time slanging match to turn around a poor display and earn victory over Switzerland in last night's friendly at the King Power Stadium.
"We could have been two or three-nil down at halftime", Tottenham Hotspur's Rose told BBC Radio 5 live.
With Dele Alli absent through injury and Jesse Lingard dropping to the bench, responsibility for giving shape to England's attacking ideas in midfield fell to Chelsea's Ruben Loftus-Cheek and Manchester City's Fabian Delph.
Of more concern to Southgate is how much football Rashford will get between now and next month's Nations League encounters with Croatia and Spain.
Having had little time to impress in a Man United shirt this season, Rashford has taken the opportunity of the global break to remind English football fans of his talent. "Harry falls in the category in which we have several players where we have to watch how much they play".
"He is happy to play wherever he can get game time and he is still getting stronger".
"I'm really pleased for him", said Southgate, when asked about the performance of Rashford.
Since establishing himself in Spurs' starting line-up at the start of the 2014-15 season, Kane has barely missed a game for club or country, clocking up 232 appearances for his club as well as for England's senior team and the U21s.
"I thought this is a good opportunity to do it", Southgate said on Monday. Playing him for 30 minutes was no big issue. And this resulted in many players taking home the prized cap, while how deserving they were of then being branded an "England international" has been open to great debate.
"He would have been a bit disappointed about the amount of time he had at the World Cup, but it was important especially to get him in the penalty box and remembering the areas he needs to be scoring goals from, and so his confidence will be boosted I'm sure, two goals against top-quality opposition in both games". To start the game is a different sort of feel, mentally it's different'.