Rashford hit a superb free-kick and ended a mazy run by finishing through goalkeeper Danny Ward’s legs after Phil Foden had doubled England’s lead in what proved to be a 3-0 stroll against their British rivals in Al Rayyan.
The 25-year-old Manchester United forward pointed to the sky after finding the net and revealed afterwards that he was paying tribute to his late friend.
He said: “Unfortunately I lost one of my friends a couple of days ago. He’s had quite a long battle with cancer, so I’m pleased I managed to score for him.
“He’s always been a big supporter of mine. He was just a great person and I’m pleased he came into my life, really.”
England are through to the last 16 where they will face Senegal, and Rashford believes Gareth Southgate’s squad is strong enough to mount a serious challenge in the knockout stages.
He added: “I feel like the ambition in the squad is really good. We have a good mix of qualities. We have a really good squad and a squad that is definitely capable of challenging to win the tournament.
“I’m hoping that we can build on this type of performance, keep improving and keep scoring goals and showing our qualities.”
Rashford was happy with the way England bounced back from their goalless draw with the United States.
He told BBC One: “We were a little bit disappointed as a team after the last game against the USA. I thought we could have played a lot better and the only way to bounce back from that is to have a good performance in your next game and I think we did that.
“First half, we defended brilliantly, we didn’t really give them any opportunities. And it was just about us killing the game off and taking the chances when they came.”
On his free-kick opener, Rashford added: “I fancied one in the first half but the one in the second half was in a better position.
“And from there, it’s just about being calm and trying to execute what you practice in training. They don’t go in often but I’m pleased that it went in today.”
Speaking about Rashford, Southgate told BBC One: “It’s great for him. He’s trained really well, I have to say.
“He’s really been impressive since he came back in with us. He could have had a hat-trick really, the chance in the first half, the one at the near post in the second. The free-kick, that is what he’s capable of, it’s an incredible strike really.”