"It's not been a ideal week by any means but we finish with a win, which is important moving forward", said Southgate.
England didn't get off the best start in the first half after making nine changes from their game against Spain, but Southgate made a few tweaks for the second half before Rashford's 54th-minute victor.
Gareth Southgate made wholesale changes from the weekend's Nations League clash, with only Rashford and Harry Maguire retaining their spots.
Alli started for the Three Lions on Saturday and completed the full ninety minutes as England slumped to a disappointing 2-1 defeat to Spain at Wembley Stadium in their Nations League opener. 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.
"It was a tall order to ask them to play against an excellent Switzerland side, they kept the ball well and we had to chase too much. We had a real jigsaw of minutes to piece together, when to put people on or take them off, and we've got them through the game". There was definitely a lot of room for improvement.
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Unfortunately, Shaw's night came to an early end after he was stretchered off following a clash of heads with Dani Carvajal . Kane, who scored six goals in seven games, was presented with the award by England manager Gareth Southgate before kick-off.
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'The gaffer had stern words with us and second half was much better'. We want to have an environment that's demanding because that's the only way we can keep raising the standards.
And they most recently played away from London when they hosted Costa Rica prior to the World Cup. We also know that, on Saturday against Spain, we could have feasibly ended with a draw which would have looked different as well.
England global and Tottenham midfielder, Dele Alli, will be available for Spurs against Inter in their Champions League group game which is scheduled to be held in a weeks time at the San Siro.
The 20-year-old's two goals will put pressure on the injured Raheem Sterling, who was preferred by Southgate in the World Cup starting line-up but is without an global goal in 26 matches.
"I imagine Croatia are having similar difficulties".