Carr said: "Freddie was training with Millwall at one of their satellite centres in Essex, so he wasn't signed to them in any way.
"To be honest, he made quite slow progress and was never a star. It was not until this season the England scouts took an interest. But, this season, he has scored more goals than games."
Sears, who hit 25 goals in those 24 reserve games, is now an England Under-19 international.
"Freddie is so down to earth. There has never been a moment's trouble from him, which makes it all the more pleasing to see him reach the first team in such style.
"All this season I have been telling him he needs to score more goals with his head. On Saturday I got a text from him saying 'Fanks for everything'."
Carr, who has been at West Ham for 35 years, joked: "Maybe his grammar isn't as good as his goalscoring or maybe I'm just getting old!"