The 20-year-old became the first England captain since Moore to lift a World Cup back in June, albeit the U20 iteration of the tournament.
Cook captained that side, with his performances leading to a surprise call-up from England boss Gareth Southgate for the friendly against Brazil on Tuesday.
England V Brazil is a fixture that has long since been associated with Moore after his sensational display against a 'Seleçao' led by the legendary Pele back during the 1970 World Cup and Cook is says he is honoured to even be mentioned in the same breath as Moore.
'It is obviously a great achievement for myself, to be named in the same sentence as someone like him,' Cook explained.
'It is a hard one. It took a while for it to sink in. I got back from the World Cup and when I got to the training ground everyone congratulated me and that is when it sunk in.
'Coming here is a great achievement too, just being around the lads is really great for me. Even if I'm just on the bench I'll just take it all in. I am really excited to be here.'
Cook's call-up to the senior squad topped off a whirlwind few days for the youngster, who had cpatained England's U21s to a 2-0 win over Ukraine just 24 hours previously.
'It has been a whirlwind few days,' he admitted.
'I was blown away and was really excited just to meet all the lads and take it all in.'
The promotion of England most talented youth players is part of the FA's attempt to establish a common 'England DNA' across all age groups and Cook feels that he must be doing something right to have been called up by Gareth Southgate.
'England are trying to get an identity of how we want to play,' he said.
'I think it's just trying to be the best we can be on the ball and trying to create something that we all can do throughout the age groups. We can see that happening with how well we have been doing.
'I feel like I must have ticked some boxes and I'm grateful for the opportunity.'