Rashford, who has struggled to find regular game time at Manchester United, has impressed his manager during the international break.
Rashford featured for England against Spain at Wembley and Switzerland in Leicester, scoring in both fixtures.
“I’m really pleased for him more than anything,” Southgate told Sky Sports after the 20-year-old scored his fifth international goal. “We know how exciting he is and we know he is going to be a top player, he’s got a super mentality and he’s great to work with.
“He’s got two goals this week, some of his performances with us have been really good but to finish with two really good finishes is very important for him.”
England did not get off to the best start and were accused of overplaying by ‘Sky Sports’ pundits.
Despite the nervy opening half an hour, Southgate was happy with his team’s second half performance.
Southgate admitted it was going to be a tough game due to the amount of players in his squad making their first starts of the campaign.
“So many of the lads were playing their first 45 minutes of the season,” said the England manager. “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.
“Their movement was really good, they kept the ball really well and we had to chase too much [in the first half]. There was definitely a lot of room for improvement.