Two-time defending champions New Zealand saw their unbeaten run at World Cups that stretched back to 2007 ended in convincing fashion by England.
Eddie Jones' ran out 19-7 winners in the semi-finals to consign the All Blacks to the bronze-medal match.
Scrum-half Smith was adamant the reverse was not for a lack of heart, though, as he compared the New Zealand dressing room to a funeral.
"I'm truly gutted and highly embarrassed," Smith said. "You've got family, friends texting you, but you know they're pretty gutted.