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.
"We could have been two or three-nil down at half-time", admitted Rose, who was man-of-the-match.
England will be back in action in October with a UEFA Nations League double trip against Spain and Croatia.
"So numerous lads were playing their first 45 minutes of the season so it was a tall order to ask them to go in and play against a really good side in Switzerland, who are an excellent team".
But after scoring in Saturday's 2-1 defeat to Spain and the victor against Switzerland on Tuesday, he can be assured he will stay in Southgate's squad for the time being. The 20-year-old is set to score this season for the club and was sent off last time out against Burnley. Everybody has got to play a part in that but the clubs own the player and they have got to do the right thing for themselves.
The game was also a reminder of just how unbearable the England band are.
Dominic Solanke, another of Southgate's favourites, has yet to feature for Liverpool this season.
England fans took to social media to vent their frustration at the fact that the Manchester United forward was not given starting opportunities for England in Russian Federation.
"He's got huge competition for places at his club so you can understand that", Southgate said.
"It's not my business to interfere with club managers, they have a hard job to do and they have big squads at the top six, huge competition for places, so Jose thinks the world of Marcus".
Southgate said: "I wasn't in there at that moment because we always give them the first three or four minutes to themselves".
However, the second half saw a notable improvement in the team's urgency and Marcus Rashford managed to grab the only goal of the game from Kyle Walker's 54th-minute cross. We have to remember that Harry, at that age, had hardly played anywhere near the same number of matches for Spurs.
"We are going to have to assess that each time".