Both Rashford and Chelsea midfielder Ruben Loftus-Cheek caught the eye to offer Southgate food for thought before the squad's departure for Russian Federation on Tuesday.
"I can consider Championship players for the World Cup", he said.
Southgate said he was delighted to have such competition for places.
Forward Goncalo Guedes staked his claim for a place in Portugal's starting line-up with two goals in the win over Algeria, which missed out on Russian Federation, at a soggy Stadium of Light in Lisbon.
England's first World Cup match is at 7 pm on Monday 18 June against Tunisia.
"Ruben we know is a super talent and it's still early for him", Southgate said.
"It's more hard and we have some serious decisions to take, but in a good way", he said.
The Rashford we saw for England on Thursday nearly looked like a completely different player to the unconfident, stressed Rashford we saw in Man United's FA Cup Final defeat to Chelsea.
"The way that I play the game I was getting picked out more with passes and I just felt more comfortable at England".
A first-team debut was handed to Trent Alexander-Arnold, while Jack Butland started in goal after missing the win over Nigeria at Wembley.
Marcus Rashford, as he showed once again at Elland Road the other night, is one of the most talented young footballers around. But three players in particular might have played unexpectedly their way into Southgate's starting eleven. That was world class.
With around 20 minutes of the game still to play, Costa Rica brought the 20-year-old defender on as a substitute. "He's still learning the game really, even as an England global, as he has so few league appearances under his belt and is incredibly raw", he said. You can see his ability to hold people off, his speed of feet, his strength when he is running with the ball. I felt like I got better service, I got the ball better. Probably try and watch my son play cricket, and be at home with the family.
"We have got to improve to reach the latter stages of a tournament and that is going to take a lot of work over the next few weeks and a huge commitment".