Having impressed during the club's training camp in Spain, both were on target as Pools routed Northern League Division Two side Billingham Town 9-0 on Wednesday.
Smith came off the bench to score a second-half hat-trick, while Green also found the net after coming on as a substitute.
Cooper believes the pair highlight the strength of the youth system at the club.
He told the club's official website: "Just as in Spain, the pair of them did themselves a credit and they're a credit to the people who work very hard in our academy structure.
"It shows that Hartlepool United are still producing good players who can handle a football and, if you get yourself a goal like Kieran and Connor did, then you get noticed."