Southgate revealed Rashford's "slight knock" upon landing in Russian Federation and a number of team-mates attempted to allay concerns, as did the forward himself.
England have an open training session between 09:30 and 10:30 (BST) in St Petersburg.
"Marcus took a slight knock, but nothing too serious", the England manager said.
"Across three weeks, we have been really pleased to get the 23 we picked through all of the sessions". "They should say there needs to be a strapline around this tournament now that says: 'We have a great pool of talent coming through but this tournament may be a bit early in terms of the development of this England squad".
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"We know each game is going to be tough but we're fully prepared for that first game".
For those of you who are of a cynical nature, you may well point out that a different England player gives a similar sounding interview before every major tournament, and in all honesty we won't argue as you'd be pretty much spot on.
"Even if we have a disaster, we will learn - and you learn most when you get beaten".
Tottenham defender Kieran Trippier will make his first World Cup appearance, with Liverpool youngster Trent Alexander-Arnold amongst the substitutes.
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Making her 21st Wimbledon appearance, 38-year-old Venus is the oldest woman in this year's tournament. Novak, ranked 171, converted six out of 11 break points en route to victory in almost three hours.
"I'd be surprised if the majority of players did not say the World Cup is the biggest sporting event in the world". This is what it is all about, is what you work hard for as a kid and spend all of those hours training. "We have all won things ourselves at our respective clubs and we want to take that onto the global stage now".
Southgate, though, has no intentions of letting anyone in and around the camp getting ahead of themselves.
The 24-year-old striker said there were no cliques within the squad that flies out to Russian Federation later on Tuesday seeking to emulate their 1966 predecessors in lifting the trophy. So we are all here with the same mentality, all wanting to win, all wanting to play. We have got to keep wanting to improve.
One cause for concern ahead of a major tournament being held in Russian Federation has to be whether or not the locals will be capable of behaving themselves with the country renowned in the past for violent behaviour when football is concerned.
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The spokesman said: "We can not get into the specifics of the letter but the wording mirrors [his] social media rants". A suspect, Jarrod Ramos, 38, of Laurel, Maryland, was arrested and charged with five counts of first-degree murder.