Indeed, while the England head coach has acknowledged the 27-year-old's qualities, he has insisted selecting him for the national team isn't something he will do lightly.
And Hodgson says it's about showing respect to those already in the frame because of their previous form.
The Three Lions boss is quoted as saying: "I'm certainly not going to pick him on the basis of 'he scored a hat-trick, so therefore he has to be in the England team'.
"Often they're not playing for England at this particular moment because there are plenty of others who have done well.
"Maybe before we start wanting to throw out the guys who have done so well for the latest shout, the latest ice-cream flavour... we should show a little bit of respect to what they have done as well."
Hodgson's comments seem very similar to those he made about West Ham skipper Mark Noble.
Neither of the Hammers duo deserve being compared to ice cream flavours or Grant Holt - but the England boss certainly makes more sense here.
There's definitely a case for Noble making the England squad, perhaps an even bigger one for Aaron Cresswell. But Carroll is behind a long list of other quality strikers and his limited playing style means he will only suit in certain situations.
Since Hodgson's comments, of course, Carroll scored a penalty for West Ham against Leicester City - but then conceded one at the other end.