If fit, Rashford is in contention for a starting role in Volgograd next week but Southgate is unlikely to take any risks with the fitness of the attacker.
"It's not something we've had to deal with really - we all get on very well and have come through the ranks together", said Kane.
"Obviously I understand you've got the Champions League and Premier League - so many big competitions - but, for me, I don't think it gets much bigger than the World Cup".
"Everybody is looking forward to getting to the first game".
"It is a World Cup - there is always going to be pressure, nerves and excitement".
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He told reporters: "We have been practising penalties, not every session, but every now and then the coaches will throw it in at the end of the session when we are maybe a little bit worn out in games after extra-time, the lads are exhausted, that's when it's going to happen".
Their arrival at the hotel was met with a strong security and media presence.
The former Crystal Palace and Everton boss feels he should still be in charge of England and, in a BBC documentary to be aired on Sunday, said: "Jealous is what I feel".
Kane, who scored 41 goals for Tottenham Hotspur in all competitions last season, will also be hoping to find the net for the first time at a major tournament.
The single was the soundtrack to England's World Cup win in 1966.
"We want to take this tournament head on", he declares.
"We hope we can send people to work the following day having enjoyed our matches", said Southgate before departing for Russian Federation.