Rashford played as a second half substitute, replacing Raheem Sterling in the win, but Kane was the hero of the night with the two goals to give his side a morale boosting win in their opening match of World Cup Group G in Russian Federation, reported Xinhua news agency.
"Maybe I'll be sitting here in four weeks with the big gold one", he quipped back.
"England are a big team with very good players but we will try to win".
Going into the Panama game, England aren't chasing the points.
He said: 'The Euros were disappointing for me, for everyone, so it was a challenge to put that right. "I'm so proud of the lads", Kane said.
■ ONLY the England players who did not start Monday's win over Tunisia took part in training yesterday.
For Harry Kane, who scored both of England's goals, they clearly were.
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He will feel like he has arrived at this World Cup and if you could have written a script for him, as an England striker and captain, then it would not be too different from the way his night turned out.
England captain Kane said he was delighted to have scored after he and the national team suffered a frustrating Euro 2016, going out to Iceland in the round of 16.
England have more to offer than just Harry Kane insists former goalkeeper Chris Kirkland.
"To be the best player in the world, you have to aim that high".
Rashford now hopes to prove himself worthy of starting England's penultimate Group G match against minnows and World Cup debutants Panama on Sunday.
The youngster is more of a poacher than anything else and poachers tend to do better in two striker formations so the Tottenham's striker's link-up play should help him tenfold. In 96 we had (Alan) Shearer, a top-class goalscorer, and this time round it looks like we have got a world-class goalscorer in Harry Kane.
I think it was even more important because of the way we went out of the European Championship two years ago. "We have not done well in recent years, so there is not much else that could go wrong".