Sterling lifted his shirt after scoring his second goal to display a tribute to Damary Dawkins, a 13-year-old member of Crystal Palace's elite player development centre who died last week of acute lymphoblastic leukaemia, four years after being diagnosed.
Sterling had stepped in and used his social media accounts to try and help find Damary a donor, but despite finding one in the United States he passed away on Sunday.
A GoFundMe page set up to help Damary's family with funeral costs has received more than £3,000 of donations following Sterling's tribute.
"Sadly it didn't match and sadly he passed away".
Sterling's first England treble gave the Manchester City forward five goals in his last three global appearances following his brace in the October win against Spain. I was looking around the crowd and everybody looked happy.
"I'm just being confident in myself, I'm trying to get in areas and take shots, not to worry about anything".
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Southgate will talk to Rice about the incident and the Football Association confirmed they will write to the midfielder to remind him of his responsibilities, but the England manager does not expect the conversation between them to be punitive in tone.
"But sometimes, when the pool is smaller, which is going to be the case for England whilst I'm the England manager, then you have to be a bit more creative in the way you think and you have to approach things and solve the problem in a different way". He has looked like that all week in training.
"I also think the goals in Spain were an important moment for him". That's why, maybe in the past, some countries like Croatia or Yugoslavia have found really bright young talents because they've said: 'Right, we haven't got huge numbers of players, so let's stick them in'.
The England Under-19 global hasn't started a Premier League game this season despite his promising performances in the cup competitions.
Southgate believes Sterling's ability to handle the adversity laid the foundation for the kind of mature performance he delivered against the overwhelmed Czechs.
"Callum has probably had a limited amount of games at Chelsea but he's the same again, every time I've seen him I've been really excited".