The Arsenal forward scored on his first return to Wembley since his decisive penalty shootout miss against Italy in July’s final defeat.
Saka was the subject of racist abuse after his penalty miss in the summer.
But on the day he turned 20, he told ITV: “The perfect birthday present for me. I am really happy we got the win and I can celebrate my birthday with this.
“I am really happy with the reception everyone gave me, it shows how proud they are of me and that meant a lot. It means a lot, it really made a difference for me. Even now I can hear fans chanting my name. It means everything to me that I know they support me.”
England boss Gareth Southgate added: “I hope [it brought] closure if it was needed [for Saka], but I don’t think there is a player in that dressing room who thinks anything but positively about what he did all summer.”
Saka also became the first Arsenal player to score and assist for England at Wembley since Ian Wright in September 1997 against Moldova.
He added: “This is what I dream about, playing at Wembley in front of my family and this crowd and scoring on my 20th birthday.”
England needed a late flurry of goals to put some gloss on the match after struggling for long periods to break Andorra down.
Jesse Lingard put them ahead after 18 minutes, but it was not until substitute Harry Kane’s 72nd-minute penalty that their dominance began to pay off.
Lingard scored a second six minutes later and Saka made it 4-0. It makes it five wins out of five for England in Group I.