Boric has had x-rays on a cheek injury, while full back Dagg suffered concussion after also taking a heavy knock early in the second half.
"We've got one or two injuries; Anthony has got a cheek injury, we don't know how serious it is. Israel has got a head injury and he's not very well," admitted Graham Henry immediately after the match.
"There's one or two other knocks, but they're the two that are particularly serious and could miss some rugby because of it."
In the Welsh camp Stephen Jones and centre Andrew Bishop both attended hospital for x-rays on potential hand injuries.
Jones was replaced by Dan Biggar in the 57th minute, while Tavis Knoyle came on for his debut with six minutes remaining as a replacement for Bishop.