Sterling provided two assists for Borussia Dortmund winger Sancho in quick succession, the teenager becoming the youngest player to score more than once in a game for England since Wayne Rooney in 2004.
"It was a good run from Raheem, he found me and I slotted it home," Sancho, 19, told ITV.
"It means a lot to me personally and for my family it is a special day.
"I dedicate the goals to my nan, who was a big fan of me but has sadly passed away."
Gareth Southgate's side responded well after a Michael Keane error allowed Valon Berisha to score the first of his two goals with just 34 seconds on the clock.
"It was a crazy game. I'm delighted to score my first goal for England," said Sancho.
"The opener was a bad mistake from us but it was a great comeback."
After the restart England conceded twice more and Sancho acknowledged there are defensive improvements needed despite a fourth Group A win out of four games.
"I think we started a bit slow [after half-time]," he added. "Next time we have to pick up on that and learn from it."